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NO. 91-80002-1 





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AUTHOR: 


UEBERWEG, FRIEDRICH 


TITLE: 


SYSTEM OF LOGIC AND 
HISTORY OF LOGICAL... 


PLACE: 


LONDON 


DATE: 


18/1 





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Ueberweg, Friedrich, 1826-1871. 


System of logic and hi 


Friedrich Ueberweg ..- 
and appendices, by Thomas M. Lindsay ... 


mans, Green, and co., 1871. 
xx, 590 p. diagrs. 223. 


“This translation is from the text 
1868, and contains all the additions 
inserted in the next German edition. 


Tr. from the German, with notes 
London, Long- 


of the third edition, published in 
and alterations which are to be 


»_Translator’s pref. 


1, Lindsay, Thomas Martin, 1843- tr. 


1. Logie. 


~~ 


““- 
Library of Congress BC15.U3 








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SYSTEM OF LOGIC 


HISTORY OF LOGICAL DOCTRINES. 


Ὑμεῖς. μέντοι ἂν ἐμοὶ πείθησθε, σμικρὸν φροντίσαντες 
Σωκράτους, τῆς δὲ ἀληθείας πολὺ μᾶλλον, ἐὰν μέν τι ὑμῖν 
δοκῶ ἀληθὲς λέγειν, ξυνομολογήσατε, εἰ δὲ μὴ, παντὶ λόγῳ 
ἀντιτείνατε. 





Socrates apud Platonem. 





Τούτων δὲ τὰ μὲν πολλοὶ καὶ παλαιοὶ λέγουσιν, τὰ δὲ ͵ 
ὀλίγοι καὶ ἔνδοξοι ἄνδρες" οὐδετέρους δὲ τούτων εὔλογον ͵ D® 7 NT + 
διαμαρτάνειν τοῖς ὅλοις, ἀλλ᾽ ἕν γέ τι ἢ καὶ τὰ πλεῖστα | FRIEDRICH UEBERWEG, 
κατορθοῦν. PROFESSOR OF PHILOSOPHY IN 


Aristoteles. THE UNIVERSITY OF KÖNIGSBERG 


Intelligitur, quod. ars illa, quae dividit genera in 
species et species in genera resolvit, quae διαλεκτικὴ 
dicitur, non ab humanis machinationibus sit facta, sed 
in natura rerum ab auctore omnium artium, quae vere 
artes sunt, condita et a sapientibus inventa et ad utili- Fr 
tatem solerti rerum indagine usitata. NSLATED FROM THE GERMAN, WITH NOTES AND 
, APPENDICEs, 


Johannes Scotus (Erigena). ‘i 


Nam normae illae: experientia, principia, intellectus THOMAS M. LINDSAY ın 
consequentiae, sunt revera vox divina. NDSAY, M.A., F.R.S.E., 
RXAMINER IN PHILOSOPHY TO THE 

UNIVERSITY OF EDINBURGH, 


Philippus Melanchthon. 


| LONDON: 
SPOTTISWOOD! τ τ ; . LON GM AN , GRE E N, AND 
1871. 


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»- ἘΞ 6) ς 
e) () 4) ὦ .} 
AUTHORISED TRANSLATION, 


containing the 


LATEST ADDITIONS AND CORRECTIONS, AND REVISED BY THE AUTHOR. 


\ or 
A b2 2 


TO 


ALEXANDER CAMPBELL FRASER, 
M.A. LL.D. F.RS.E,, 


PROFESSOR OF LOGIC AND METAPHYSICS IN THE 
UNIVERSITY OF EDINBURGH, 


THIS ATTEMPT 
TO FOSTER THE HIGHER STUDY OF LOGIC 
BY THE TRANSLATION OF 
ONE OF THE BEST GERMAN MANUALS, 


IS DEDICATED 


BY 


AN OLD PUPIL. 








TRANSLATORS PREFACE, 


— 


PROFESSOR ÜEBERWEG’S ‘ System of Logic’ enjoys a 
popularity among German students which is shared by 
no other manual. It has already reached three editions, 
and will soon appear in a fourth. Acquaintance with 
these facts, personal experience of the value of the 


book, and the knowledge that there is no really good 


logical text-book for advanced students in our lan- 


guage, led me to undertake this Translation. While it 
is not especially intended for beginners, and while the 
student is recommended to make himself previously 
familiar with the outlines of Logic as given in such 
excellent little books as those of Fowler or Jevons, 
some judicious ‘skipping,’ in the more difficult parts, 
will bring this manual down to the level required. by 
those who begin it entirely ignorant of the science. 
This Translation is from the text of the third 
edition, published in 1868, and contains all the addi- 


tions and alterations which are to be inserted in the 





Vili Translators Preface. 








next German edition. Although I am responsible for 


the translation, and liable to censure for its many 
faults and defects, it is but right to mention that 
anyone who compares it with the original will find 
numerous small omissions, additions, and alterations— 
indeed, there are few pages which do not differ in 
some particular from the text of the third edition,— 
all of which have been made by the author. Dr. 
Ueberweg has himself revised the sheets ; and, as he 
knows English well, this Translation may be held to 
give his opinions as he wishes them expressed in our 
language. 

In order to make the book more useful to students, 
the opinions of the more prominent English logicians 
on the points discussed have been from time to time 
inserted. Such passages are distinguished by the 
brackets [ ]. For these and for the first three Ap- 
pendices I am alone responsible ; but my friend Pro- 
fessor W. R. Smith has furnished the account of the 
late Professor Boole’s logical opinions in Appendix A. 
Appendix D will appear in the fourth German edition, 
and has been added in deference to the author’s wishes. 

It need only be added, that while agreeing in the 
main with the logical opinions .of Professor Ueberweg, 
I must not be held responsible for every theory ad- 


vanced in the text-book, and must dissent from some 





Translator's Preface. ix 





of the statements regarding the Logic of Mathematics. 
The remarks made at page 577 in Appendix A seem 


almost as applicable to Dr. Ueberweg’s views as to 
Mr. Mill’s. 


Tuomas M. Linpsay. 


7 GREAT STUART STREET, EDINBURGH: 
June 1st, 1871. 


NOTE.— Since writing these lines the sad and unexpected 
news of Dr. Ueberweg’s death has reached me. These pages 
will have a mournful interest to his many friends, for their 
revisal was the last bit of work he was able todo. He had 
just finished them when death ended his labours. 


T. BE I; 
June 15th. 











AUTHOR’S PREFACE 


THE FIRST EDITION. 


SCHLEIERMACHER, whose philosophical significance has but too often been 
overlooked for his theological, in his Lectures upon ‘ Dialektik’ (ed. by 
Jonas, Berlin, 1839), sought to explain the forms of thinking from science, 
which is the end and aim of thinking, and to make good his opinion by 
proving their parallelism with the forms of real existence. This appre- 
hension of the forms of thought holds a middle place between the sub- 
jectively-formal and the metaphysical Logics, and is at one with the 
fundamental view of Logic which Aristotle had. The subjectively-formal 
Logic—that promulgated by the schools of Kant and Herbart—puts the 
forms of thought out of all relation to the forms of existence. Meta- 
physical Logic, on the other hand, as Hegel constructed it, identifies the 
two kinds of forms, and thinks that it can recognise in the self-develop- 
ment of pure thought the self-production of existence. Aristotle, equally 
far from both extremes, sees thinking to be the picture of existence, a 
picture which is different from its real correlate and yet related to it, 
which corresponds to it and yet is not identical with it. 

Ritter and Vorländer! have worked at Logic from the standpoint 
of Schleiermacher: the investigations into the theory of knowledge 
of most of our modern logicians, who do not belong to any definite 
school, lie more or less in the same direction. Trendelenburg, who has 
revived the true Aristotelian Logic, comes in contact in many ways 
with Schleiermacher’s Platonising theory of knowledge, without being 
dependent? upon him, and has a basis of metaphysical categories 
acquired independently in a polemic against Hegel and Herbart. The 
view of Lotze is more distantly related. It approaches nearer to Kant’s, 
and represents that in the laws and forms of thought only the necessary 
metaphysical presuppositions of the human mind upon nature and the 
universe mirror themselves. Essentially accepting Schleiermacher’s 
fundamental axioms concerning the relation of thought to perception 


* Now (1868) also George. (Added to the third edition.) 
* At least without any direct dependence. Schleiermacher’s Lectures on Dialectic, 
published in 1839, are only quoted here and there. But the influence of Ritter’s 


Logic apparently shows itself in his doctrine of the notion and of the judgment. 
(Added to the second edition.) 


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ΧΙ Authors Preface to the 





and of perception to existence, Beneke has proceeded to blend these 
with his psychological theory, partly constructed after Herbart’s, into a 
new whole. 

This present work on Logic proceeds in the direction denoted by the 
labours of these men, while conscious of the right of complete 
independence in the mode of procedure. It sets before it both the 
scientific problem of aiding in developing Logic, and the didactic one of 
assisting to its study. 

In the first reference, the Author hopes that he may succeed in the 

resent work in answering the principal questions relating to the 
problem, sphere, and arrangement of Logic, and to the standpoint from 
which Logic is treated as a theory of knowledge, and in furnishing a 
not worthless contribution to the solution of many single problems. 
Polemic is used sharply enough where occasion demands, but only 
against those of whom I can say with truth—‘verecunde ab illis 
dissentio.’ That truth was the single interest, determining me in each 
case to agree with or contradict, need not require previous assurance, 
but will appear from the work itself. On my side, I will welcome 
every thoroughgoing criticism as heartily as agreement. One thing I 
do not wish, and that is, that this independently thought-out work be laid 
aside by classing it under this or that general formula—Empiricism, 
Rationalism, Eclecticism. For this would falsely represent my work to 
be the mere exposition of a one-sided antiquated party standpoint, or, 
since it is essentially related to the whole of the philosophical tendencies, 
would accuse it, mistaking its leading fundamental thought, of want of 
principle. The Author would least of all object to have his system 
entitled an Ideal-Realism. 

In the didactic reference, I have striven to exhibit general Logic 
clearly, exactly, comprehensively, and so far completely, as a theory of 
knowledge, and to describe the ‘chief moments in its historical develop- 
ment. What is universally recognised has been rendered in a precise 
and strictly systematic form. What is doubtful and debatable will be 
explained, not with the prolixity of the monograph, but with a sufficient 
consideration of the points which decide the question. A systematic 
representation of scientific Logic must, in so far as it is meant to serve 
as a text-book to those entering upon the study, presuppose genuine 
students of science, who do not mean to shirk difficulties, but to over- 
come them. Particular parts may always be passed over in a first 
study. ‘These will meet the want of those who, already familiar with 
the elements, may wish to extend their studies. The examples will 
show the importance of the logical laws in their application to all 
the sciences. Finally, by means of historico-literary examples and 
investigations, in which the Aristotelian point of view of thankful 
reference to all essential moments of development of scientific truth is 


preserved, this work strives to encourage the most many-sided study of 


Logic possible. 


Bonn: 
August, 1857. 


Second and Third Editions. 


τυ 


THE SECOND EDITION. 


I might recommend this work more especially to the attention 
of those engaged in the investigation of Nature as a thorough-going 
attempt at a comparatively objective theory of knowledge in opposition 
to Kant’s subjective criticism. It may serve to give a philosophic 
basis to their more special methodic. The kernel of my opposition to 
Kant lies in the thoroughgoing proof of the way by which scientific 
insight is attained, an insight which mere experience in its immediate- 
ness does not warrant, which is not brought about by a priori forms 
of purely subjective origin, finding application only to phenomenal 
objects present in the consciousness of the subject (and has not, as 
Hegel and others desire, an a priori, and yet objective validity ) but is 
reached by the combination of the facts of experience according to the 
logical rules, which are conditioned by the objective order of things 
and whose observance ensures an objective validity for our knowledge. 
I seek more especially to show how arrangement, according to time 
space, and cause, on whose knowledge apodicticity rests, is not first of 
all imposed upon a chaotically given matter by the perceiving thinking 
subject, but is formed in the subjective consciousness in accordance 
with the (natural and spiritual) reality, in which it originally is, suc- 
cessively by experience and thinking 





THE THIRD EDITION. 


εν « . University education and its lectures, to bring forth good fruit 
must presuppose a knowledge of the elements of Logic, and a familiarit 
with them such as is only to be got by school training. Philosophical 
propaedeutic is of value in the studies of the gymnasia, both as a very 
suitable conclusion to intellectual education, and more especially as a 
means in the teaching of one’s own language and literature, . . . I have 
exerted myself in the present third edition of this book not only to in- 
crease its scientific value by a more acute treatment of many problems 
and by a thoroughgoing reconsideration of newly-risen difficulties but, 
more than hitherto, by the kind of explanations and the choice of ex- 
amples, ‚to supply the needs of the teacher who gives preparatory 
instruetion, and to meet the wants of the student for whom it is to 
serve as a solid foundation for philosophical instruction 


KOniGsBEre : F. UÜEBERWEG. 


September, 1868. 











CONTENTS. 


πος --τ- Oe 





INTRODUCTION. 
Notion, Division, and General History of Logie. 


DEFINITION oF Logic , ‘ : 

The forms of knowledge. Their dunks alien Their rela- 
tion to the contents of knowledge 

The end and aim of the activity of knowledge. Tr ‘uth. Se entific 
knowledge . : 

The possibility of Logic ai as a science 

The absolute and EEE worth of Logic 

The place of Logic in the system of Philosophy 

The study of Logie as a propaedeutic for other philosophical 
studies 

DIviston oF Logic. 

The value of the mıstory oF Los 

The historical origin of Logic . 

The Ionic natural philosophers, the Py thagoreans, and the 
Eleatics . 

The Sophists and Sokrates 

The one-sided Sokratie Schools 

Plato ‘ ; 

The Platonists 

ARISTOTLE. 

The Peripatetics ; 

The Epikureans, Stoics, and Skeptics 

The Neo-Platonists . ‘ 

The Christian Fathers. The Study of Dialectic i in the Schools 
among Christians, Arabians, and Jews 

The ἜΣ 

The earlier times of the ΜΕΝ ΤΕ 

Bacon of Verulam 

Des Cartes 

Spinoza . 

Locke . ‘ 

Leibniz and Wolf 





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Contents. 


Kant : ; : 
The Kantian School and allied ἡδέως Fries. Herbart 
Fichte, Schelling, and their School . 

Hegel . 

The Hegelian School 

Schleiermacher 

The latest German logicians 

Modern logicians beyond Germany . 





PART I 


Perception in its relation to Objective Existence in 
Space and Time. 


DEFINITION OF PERCEPTION 


A.—EXTERNAL OR SENSE-PERCEPTION. 


Arguments against the agreement of sense-perception with 


what actually exists without . . 
The incorrectness of the Kantian separation of the matter and 


form of perception 


Upon the capacity to know the existence of object affecting 
us grounded on sense-perception . 


B.— INTERNAL OR PSYCHOLOGICAL PERCEPTION. 


The agreement of the inner perception with the perceived 
reality 


C.—THE CoMBINATION OF OUTER AND INNER PERCEPTION. 


The knowledge of the plurality of animate existences 
The knowledge of the gradual series of existences—Science, 


Faith, Presentiment, Opinion, &c. 
The reality of Matter and Power 
The reality of Space and Time 


PART II. 


The Individual Conception or Intuition in its relation to the 
Objective Individual Existence. 


DEFINITION OF INDIVIDUAL CONCEPTION OF INTUITION. 
The distinction of individuals by means of individual con- 


ceptions 


. 110 


21 


$ 67. 


Contents. XVil 


The forms of individual conception and existence. The CATE- 
GORIES in the ARISTOTELIAN sense. The parallelism between 
the forms of individual existence, forms of conception, and 
the parts of speech 

Clear and distinct conception . 

Attributes—The parts of a conception 

The content of a conception. Its partition 


PART III. 


The Notion according to Content and Extent in its relation 
to the Objective Essence and the Genus. 


Attention and Abstraction. The General Conception 
Determination . ‘ ‘ : ; ; ‘ : 
Extent. Division. The relations of conceptions to each other 
according to extent and content . : ν᾽ ‘ . 
The relation between content and extent. 
The graduated series (pyramid) of conceptions 
DEFINITION OF THE NOTION. The essence ; : 
The knowledge of the essential. The ἃ priori and ἃ posteriori 
elements in the formation of the notion 
Class, Genus, Species, &c. Their oe and their knowabilt 
The individual notion 
DEFINITION. 
Difference . 
The Kınos of definition ’ 
The most notable faults in definition i ‘ ; ᾿ 
Division. The ground of division. The members of division : 
Dichotomy, Trichotomy, &c. 
Subdivision, and co-ordinate division 
The most nadie faults in division . a 
The connection between the formation of ia ὦ tie other 
functions of cognitive thinking 








Faas i. 


The Judgment in its reference to the Objective Fundamental 
Combinations or Relations. 


The DEFINITION OF THE JUDGMENT 


§ 68. Simple and complex judgments. The individual relations of 


the judgment, and their reference to the corresponding 


a 


PAGE 


. 114 
. 125 
. 125 
. 126 


. 187 























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Contents. 


PAGE 
relations of existence. The Carreortzs of RELATION in the 
KANTIAN sense . . ‘ ; ‘ . . 195 

Qvarıry and Monarıty of judgments. ’ ‘ . . 206 

QUANTITY of judgments . ; . . 214 

Combination of divisions according to Quality and Quantity. 
The four forms of judgment A, EK, I, and O : : . 216 

Contradictory and contrary opposition between two judgments. 
Subalternation . , 

The Matter and Form of judgments 





PART V. 


Inference in its relation to the Objective Reign of Law. 


DEFINITION OF INFERENCE 

THE PRINCIPLES OF INFERENCE in general 

The axiom of Identity 

The axiom of Contradiction . . ; ‘ 
The axiom of Exeluded Third or Middle between two judg- 


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ments opposed as contradictories , ‘ : 

The combination of the axioms of Contradiction and Excluded 

Third in the principle of Contradictory Disjunction 
The relations between judgments whose predicates are opposed 

as contraries. Dialectical Opposition. The axiom of the 

Third lying in the Middle between two contrary opposites. 

The axiom of the union of coincidence of opposites . . 278 
The axiom of sufficient reason . ; ‘ ‘ ‘ ‘ . 281 
The forms of IMMEDIATE inference in general . ‘ i . 287 
The analytical formation of the judgment. The synthetic 

formation of a judgment . i ; . ς . 289 
Conversion in general. Its internal authorisation Ξ ‘ . 294 
Conversion of the universal affirmative judgment . : . 297 
Conversion of the particular affirmative judgment . : . 304 
Conversion of the universal negative judgment : , . 800 
The impossibility of the conversion of the particular negative 

judgment . . : : : : . . 911 
Contraposition in general. Its inner authorisation : . 915 
Contraposition of the universal affirmative judgment : . 314 
Contraposition of the universal negative judgment . . 317 
Contraposition of the particular negative judgment . : . 318 
The impossibility of the contraposition of the particular affirma- 

tive judgment . ; ; . 319 
Change of Relation ; . 823 
Subalternation ; . A ‘ . 325 


Contents. 


(Qualitative) AEquipollence 
Opposition . . 
Modal Consequence . 
MEDIATE INFERENCE. Syllogism and Induction 
The simple and complex syLLosısm. The parts of the syllogism. 
Their relation ; : ; ’ . . ; 
Syllogism as aform of knowledge. Its relation to the real 
reign of law ‘ : : : νἀ 
The Sımpte Categorical syllogism. Its three terms πὰ τς 900 
The three chief classes (figures in the more comprehensive 
sense), or four divisions (figures in the narrower sense) of N 
the simple categorical syllogism . : . 352 
The different forms of combination of the premises. The 
Moods ‘ . ‘ R é τ} ‘ 377 
Comparison of spheres as a criterion of capability for inference 379 
Ex mere negativis nihil sequitur. The forms of combination 
KE, OE, EO, OO, cut off . ; : : ‘ oe 38 
Ex mere particularibus nihil sequitur. The forms of combina- 
tion II, OI, IO, cut off ‘ ‘ : ; : 
The combination of a particular major premise with a negative 
minor does not give an inference. The form of combination 
IE cut off . : ᾿ : : : ν : ; . 388 
The First Figure in the stricter sense. The forms of combina- 
tion IA, OA, AE, AO, cut off . . ; : . 391 
The First Mood of the First Figure :—Barbara ; . 804 
The other Moods of the First Figure :—Celarent, Darii, Ferio . 408 
The Second Figure. The forms of combination IA, OA, AA, 
AI, cut off. Ἶ : ‘ : \ . 411 
The valid Moods of the Second Figure :—Cesare, Camestres, 
Festino, Baroco . : ' . : : ; A : 
The Third Figure. The forms of combination AE and AO 
cut off A . : . . . . 
The valid Moods of the Third Figure :—Darapti, Felapton, 
Disamis, Datisi, Bocardo, Ferison - : ; : 
The Fourth Figure. The forms of combination OA, AO, AI, 
cut off , ‘ : . : 
The valid Moods of the Fourth Figure, or of the second division 
of the First Figure in the wider sense :—Bamalip, Calemes, 
Dimatis, Fesapo, Fresison . ‘ : : . : 
Comparative view of the different Figures and Moods. The 
form of the conclusion. The Moods Barbari, Celaront ; 
Cesaro, Camestros; Calemos. The relative value of the 
different forms. The names of the whole of the Moods . 435 
The Modality of the Syllogism . ; ; . . 439 
The Substitution of one notion for another in an objective or 
attributive relation. The syllogism from two simple 











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Contents. 


categorical judgments reduced to the Principle of Substi- 


tution . 
The syllogism from subordinately complex and especially from 


hypothetical premises. ar 

Mixed inferencesfroman hypothetical and a categorical premise, 
or the so-called Hypothetical Syllogism . 

Mixed inferences with co-ordinate opposed premises, and espe- 
cially with a disjunctive premise. The Dilemma, Trilemma, 
Polylemma, or the so-called Horned Syllogism . 

Complex Inferences. The chain of inference. The Prosyllo- 
gism and Episyllogism . 

Simple and complex inferences expressed in an abridged form. 
The Enthymeme. The Epicheirema. The Chain Syl- 
logism, or Sorites ‘ , ; . 

Paralogisms and Sophisms agai gyi aaa ni. ERRATA. 


ae ww ö ᾿ : i i ‘ ; ᾿ Page 4, line ὅ, for content read contents. 

jon . - { ‘ : - ; ; . = 5, „ 25, for Euklid read Euclid. 

Imperfect Induction . . . . . . . . » 16, note 2 should be within brackets. 

The most notable errors in Induction „ 49, line 3, for Skepticism read Scepticism. 

Inference by ANALOGY . ᾿ i ; | „ = = 5, delete [Best edition by T. H. Greene, &e.) . 
Determination of DEGREES OF PROBABILITY ιν καὶ 4 FEW subject read added by the subject. 


The MATERIAL TRUTH of the premises and of the conclusions . 76, note ! should be within brackets. 
196, line 11, delete the comma after ‘ case.’ 


HypotTHEsIsS . ; ‘ . ‘ ; \ ὶ , ‘ 
PROOF 925, ,, 16, for give read gives. 
235, „ 9, for THE (avoidance of) read (the avoidance of). 


Refutation. Investigation. Problem . : 274, „ 17, for popositions read propositions. 
The most notable errors in Proof 359, ,, 13, for anology read analogy. 


PART VI. 


System in its relation to the Order of Objective Totalıty 
of Things. 


DEFINITION or System. The law of thought of the totality . 
The Principle. Analysis and synthesis 

The analytic (or regressive) method 

The synthetic (or constructive) method . 


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Appendix A. On recent logical speculation in England 
Appendix B. On the Quantification of the Predicate . 
Appendix C. On the doctrine of the Essence . 5 
Appendix D. On the fundamental principles of Ethics 





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SYSTEM OF LOGIC. 


-----οοἱδῖοο.---- 


INTRODUCTION. 


1HE NOTION, DIVISION, AND GENERAL HISTORY 
OF LOGIC. AS? 





§ 1. Loarc is the science of the regulative laws of human 
knowledge. ‘The act of knowing is that activity of the | 
mind by means of which it consciously reproduces in| 
itself what actually exists. The act of knowing is 
partly immediate or outer and inner perception, partly 
mediate or thinking. The regulative laws (injunctions, 
prescriptions) are those universal conditions to which 
the activity of knowledge must conform in order to attain 


to the end and aim of knowledge. 


πὶ 


Logic, as the doctrine of knowledge, occupies the mean 
between what is commonly called formal, or, more definitely, 
subjectively-formal Logic, which treats of the act of thinking 
apart from any relation to objective existence, and Logic 
identified with Metaphysics, which would represent along with 
the laws of the act of knowing, the most universal (metaphysical 
or ontological) contents of all knowledge. This middle position 
is described and justified in $$ 3 and 6, and in the sketch of 
the general history of Logic, especially in $$ 28-35. | 

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δ 1. Definition of Logic. 


Knowledge, in the wider sense in which we here use the 


word, comprehends both cognition, which rests on perception 


(and on the evidence transmitting perceptions of which we are 


ignorant), and also knowledge in the stricter sense, which is 
attained by thinking. | 


The act of knowing, in so far as 


it is the copying in the 
hum 


an consciousness of the essence of the thing, is an after- 
thinking of tre thoughts which the divine creative thinking 
has built into things. In action the preceding thought deter- 
mines what actually exists, but in knowing the actual exist- 
ence, in itself conformable to reason, determines the human 
thought. 

Plato declares that know 


a a . Φ 1 
ing 15 conditioned by being. 
Aristotle says 


almost the same in reference to 


; the judg- 
ment:? ἔστι δὲ ὁ μὲ 


> ‘ / A " m 
ν ἀληθὴς λόγος οὐδαμῶς αἴτιος τοῦ εἶναι τὸ 
πρᾶγμα; τὸ μέντοι πρᾶγμα 


/ / v La} 3 ᾽ aA 
φαίνεταί πως αἴτιον τοῦ εἶναι ἀληθῆ 
τὸν λόγον" 


A \ 8 x \ La) x \ IA 07 e ’ . x 
Τῷ yap εἰναι TO πρᾶγμα ἢ. μὴ ἀληθὴς ὁ λόγος ἢ 
: δὲ TR 3 ’ x, x e \ ‚ 7 
ψευδὴς λέγεται. ἀληθεύει μὲν ὁ τὸ διῃρημένον οἰόμενος διαι- 

~ / A Ν 
ρεῖσθαι καὶ τὸ συγκείμενον συγκεῖσθαι, ἔψευσται δὲ ὁ ἐναντίως 
bd δι Ν ΄ > ᾽ \ ὃ \ N e a ΕἾ] > - 
ἕχῶν ἢ τὰ πράγματα" . .. οὐ γὰρ διὰ τὸ ἡμᾶς οἴεσθαι ἀληθῶς 
\ 3 . \ \ - 
σε λευκὸν εἰναι εἶ σὺ λευκὸς, ἀλλὰ διὰ τὸ σὲ εἶναι λευκὸν ἡμεῖς 

e ΄ lal ’ , nw 
οἱ φάντες τοῦτο ἀληθεύομεν." τρόπον τινὰ ἡ ἐπιστήμη μετρεῖται 
τῷ ἐπιστητῷ. 

‘ « 

Schleiermacher® says: 


‘To the proposition that thinking 
must conform to being 


» must be added another, that being 
must conform to thinking. The latter proposition is the prin- 
“ciple and measure for every activity of the will, the former 
for every activity of thought.’6 

Lotze’s remark that mind is better than things, 
need to be their mirror in knowledge, does 
logical principle, because—1. 


and does not 
not invalidate our 
The objective existence to be 


' Rep. v. 477, ed. Steph. * Arist. Cat. xii. 14 5, 18, 

> Arist. Metaph. ix. 10, § 2’ed. Schwegler., p- 1051 B, 3 ed. Bek 
* Arist. Metaph. x. 6, 18, p. 1057 a, 11. 

5 Dialektik, ed. by Jonas, p. 487. 


6 Cf. Schelling, System des transscendentalen Idealismus, 1800, p. 
13 ff; Hegel, Encycl. § 225. 


ker, 


a 


΄ 


j 5 Η 
; mh οὗ 
ὃ oft ot Le STE 2 
J (AY ᾧτε 2 nie 
PAL ™ ; < 
/\ FF ἃ, 2 ( 1 


3.2. The Forms of Knowledge, ete. 3 














Iso (as in 
-nown consists not merely of natural arte but a >> 
En &c.) of mental contents. 2. The ie are er ; 
ness, although reproduction, cannot be gers: Ge ταὶ 
peculiar activity of the mind. 3. The whole a ae 
ind is not exhausted in knowledge. There is bes > 
γον power of the phantasy, reforming and πρηνής wha 
er é | | 
en rn en κε δ: jae le only 
The definitions in the ıntrodu to we 
nitions, and their enunciations as thes ἱ 
pincers rs in Ξε independent investigation (e.g. in § 37). 


§ 2. Since the human mind must consciously repr υ 
7 snowing 18 
duce what actually exists ($ 1), the act of knowing = 
jecti 7 assen 
conditioned in two ways: a. Subjectively, by the μὰ 
| ially 108e 
and natural laws of the human mind, especially by t 
< « ει c : ὶ ' 
f the human powers of knowledge ; b. Objectively, 
O c ik i 
(ΠΟΥ͂ ısti 
by the nature of what is to be known. The = 
{ ar a8 
tutions and relations of what is to be known, = 
-esentation in the ac 
these require different ways of representation 1n e 
‚istenc ence 
ine, we call forms of existence (e.g. subsist 
of knowing, τ; ; re 
and inherence). The notions of these forms > 
Ue ifferent 
ence are the metaphysical categories. The diff | 
or iste in 
ways, corresponding to these forms of existence, " 
A ists 1 ν nie 
which what actually exists is taken hold. of and coy 
the forms of knowledge (e.g. 
in the act of knowledge, are ἢ 
the categorical judgment). The actual copy, the be 
ae £ knowledge, is the content of knowledge. 
of the activity ὁ ge, ara > 
i f the forms of knowledge are the log 
The notions of the | rn 
categories. Since the laws ot knowing, as such, de | 
| forms 
only the ways of representation (copying ), or ne = 
<plained to; 
of knowledge, not its contents, Logie can be ~ : Mt 
‘ x nowledge. in 
be the doctrine of the laws of the forms of know ᾿ e 
ic 1 "mal sci - since the forn 
this way Logic is a fo mal seience; but 
B 2 





» 


Yj, Lay γῇ, . IF PER: 
2 A . ER a yo , j 

N 7 fi 4 4 

4 ; ͵ / f i é 


3. End and Aim of Activity of Knowledge, etc. 5 








4 § 2. Lhe Forms of Knowledge, ete. 


St 


Logic is formal because it is the doc- 
thinking, even if this form 
f the con- 








relation to the actual. 


trine of the correet form or way of 
is conditioned by the endeavour after an agreement 0 
tents of thought with actual existence. It is Subjectively-formal 


Logic which directs its attention exclusively to the subjective 
agreement of thinking with itself. 

Kant and his school have connected the distinction of formal 
Logic, in the sense that it exhibits only the laws of analytical 
knowledge, and the criticism of the pure reason, which inquires 
into the possibility of a universally valid synthetic knowledge, 
with the distinction of the analytic and synthetic formation of 
judgments (ὃ 83). The Aristotelian Logic is an analytical 
theory of thinking, but the formal Logic, in the Kantian sense, 
a theory of analytical thinking. 

Beneke’s distinction of analytical or ‘ logical’ thinking from \ 
the synthetic elements of thinking, and Ulrici’s division of | 
thinking into productive (synthetic) and separative (analytic), 


are related to Kant’s. 
It does not seem proper t 


is valuable and true in connection w 
ments, should be raised to be the principle of a division of the 


whole of Logic into two separate parts. This procedure would 
be like a geometer’s, who divides his science into two separate 
divisions, as its propositions could be proved with or without 
the eleventh axiom of Euklid. Such methods of treatment 
have their full scientific value as monographs on single axioms, 
but cannot determine the whole articulation of a system, which 


must rest on a more comprehensive point of view. 


which it treats of correspond to the forms of existence 
they are conditioned by the objective realit They 
stand in essential relation not only to the τὰ { of 
knowledge in general, but also to the particular ch : 
of the contents in the modifications they take for σὸς 
time being. wih 


Logic h \ 
a . 
ee s both a metaphysical and an anthropological si 
inasmuch as it is founded pological side, 
rosea aed upon the universal laws of existence 
< als = . 
element => the laws of the life of the mind These t 
ments, howev ; . e two 
τ᾿ se a ever, do not make independent parts of logic, but 
y serve for the foundation of the reculatiy gic, 
are consequently, in the treatment of i = dh ee. 
é it of individual : 
art concer | Ä al portions of th 
cerned, to be borrowed from Psychology and Met ‘ 
ΓΟ 1 ae γ - R LV. a? 
: thi s as auxiliary axioms, or to be explained onl ὕω = 
as this 1s necessary in so 
aa mre for the purpose of Logic Losi: doe er 
ec Y reat 0 Bein» No 2 BR. δ s no 
EBEN g, Essence, Causality, the moving cause 
‘ieee = » &c., nor yet of the principles of Psychol 2 
é ore th; - : og 
ise εἶθ does Dietetic the chemical and physiolo ad 
Sses ; it ec: : : 21Ca 
tory o foll ut ıt can refer to such investigations as prep: 
y or ioillowiıne, At th : 5 para- 
those regarding the pos rg > — Investigations as 
aD oO 55 Or K 1 1 . 
the validity of our noti τῇ nowing things, regarding 
not to | notions of Space, Time, Causality, & τ 
io he ote é 7, &e., a 
2 ee from Logie,! for these eh ἐν 
tn r k , . av 
our knowledge, not with the form en e 
such. S of existence as 
The relati - 
«110 N . 
== on of subject and predicate in the catecoric 
Judgment to the forms of existence, subsist d i un 
or the relati ee : stence and inheren 
wae 1 : “ya of superordinate and subordinate notions t he 
“9 - rere: 18 
ἋΣ in which things exist in genera nied f o the 
visionally serve to eive a ὥς 3 Species—may pro- 
: Θ arer idea of th ὃ 
: , : e 
between logical and metaphysical or ontological] ἢ ae 
8 orms. .$ 8 


hat a distinetion, which of course 
ith the formation of judg- 


\ 


§ 3. The aim of knowledge is TRUTH. Knowledge \ 


arrived at the certainty of truth is scrence. Material ~ 
(or real) truth must be distinguished from (formal) 
Material truth in the absolute sense, 


correctness. 
agreement of the content of 


Lo as , ) y 


ee 7 1 ] 
a As er thinks, Zog. 3rd ed. pref. Ρ. Xvi 
E.g. Steinthal Berlin Ρ 
g. 8 » Gram. Log. and Psych. (Berlin, 1855), p. 146. 


or simply truth, 1s the 
knowledge with what actually exists. 


in the re 


Material truth 


lative sense; or phenomenal truth, is the 





γι 
Zn ᾿ 
“Ὡς 4 d 


Knowledge. Truth. 


Sciente. ἢ 7 








6 § 3. End and Ain of the Activity of 


— 


The explanation 








all their differences, is insufhicient.’! 
scendental truth, as the orderly arrange- 


goes as far on the other side: ‘ Veritas, 
pellatur et rebus ipsis inesse intel- 
6 enti conveniunt.”” 


from 
of the so-called tran 


ment of: real objects, 
quae transscendentalis ap 


ligitur, est ordo eorum, qua 
In so far as Logic seeks to determine whether and how far 


the content of knowledge and objective 
it is a critique of knowledge. In so far as 
which the measure of agreement 
Logic in the stricter sense. 


agreement it ’ 1 
with the hehe κα δῖον ἜΜΕΝ thought 
er ner perceptions which 
exist when the soundness of the mind and of tl 
bodily organs is undisturbed, or would exist u i 
the corresponding outer conditions. Pr . 
oO 
agreement between 
reality is attainable, 


it teaches the procedure by 
attainable is actually attained, it is 
In the doctrine of perception the one side, and in the doctrine 
of thought the other side of Logie is the prevalent. Without 
inner contradiction, general criteria can be found accord- 


any 
ing to which the agreement of a plan, a picture, a notion, ἃ 
The refer- 


some iCli 1 
a e logicians formal truth is the absence of conti 
ic ° = 
tion, or the agreement of th 
rn ee oughts with one 
sue r. Material truth includes formal. in the seı 
= | ae al, 186 
absence of contradiction ; but there may be the ab 
sence 4) N er . . a 5 
- of contradiction without material truth. In the 
uller sense | 
sense of the term, formal trutl Ι 
1 or correctness is 


the Co 2] TON ΕΑΔ 1 τ] 
aie a of the activity of knowledge with its 
ogical law "he : Ww 
- a | aws. When the form of perception, as well as 
i | | 5 « « 
inking, meets all the logical demand 
the relative) material trutl Ἵ ren 
aterlal truth must exist; 
| xist; and formal cor 
rectness 5 | τά. 
ess 5 the fuller sense guarantees this. But cor 
rectness of thougl | 
ıt only warr 
g rrants that th 
cee | é e connection 
5 ne the antecedents and consequents is know1 
it really is, wi ᾿ Ἶ 
, is, with truth, and that therefore where the 
antecedents have ‘le 
| ea have material truth the consequents have it 
also. With respect theref 
| 1erefore to the ai 
ith aim and end of k 
ee sia of know- 
40 ? > = Ὁ 3 
: » Logie is the scientific solution of the question relatin 
O ie crite 7 Ὰ a . . f | 
= ıterıa of truth; or, the doctrine of the requlati : 
aws, on whose observance res satt a 
Br ‚ance rests the realisation of the id 
) 3 . [2 [2 ’ 
of truth in the theoretical activity of man Ἴ 


In opposition to truth in the loei 

the thoug a res . gical sense—the agree 

zu Lape object, and supplementary ῥα en 

een με of the word—the correspondence of the object 

ef an ge The explanation Pet 

Pay , ruth, as ‘the harmony of knowledge wit] 
complete abstraction from all objects τὐλυκον ye 

é an 


proposition, &c. W 


ith its objeet can be decided. 


ence, what the particular objects are in each case, first comes 


in the application. 


Scepticism and the Critical Philosophy raise weighty | 


ctions against the possibility of arriving at and being 
In order to be assured of truth in 
the absolute sense, we must be able to compare our conception 
with its object. But we never have (says the Critical Philo- 
sophy) the object otherwise than in our conception; we never 
have it pure in itself. We only compare our conceptions 
with our conceptions, never with the things in themselves.’ 
Material truth in the relative sense succumbs to the difficulty 


which the old Skeptics expressed in the question: Tis κρινεῖ TOV 
ρινῶν τὸν ὑγιαίνοντα καὶ ὅλως τὸν περὶ ἕκαστα 

Formal validity, lastly, in the sense of 
arry us beyond what we, 
e get at the 


obje 
certain of material truth. 


ὑγιεινόν ; or τίς OK 
κρινοῦντα ὀρθῶς ?° 
absence of contradiction, does not ὁ 
at least implicitly, possess already. How then dow 
first knowledge, and how can we advance in knowledge ? To 


these general difficulties are to be added particular ones 
belonging to single forms of knowledge, which will be men- 
1 Kant, Log. ed. by Jiische, p. 66. 
2 Christian Wolff, Ontolog. ὃ 495. 
3 Arist. Metaph. iv. 6, p- 1011, A, 5. 








8 : £ 
mre. 3. 3. End and Aim. of the Activity of 
ν nn ards. Their solution is the problem of the whole 
J ee 0 : ogic, and cannot therefore be given in this place.! 

as . . ΝΞ ' 4 . 
Sx s En urged against the identification of Logic with th Ε 
in . ἔς . > | 
a Pe regulative laws of human knowledoe that the 
é Μ ; ’ 
2 en ne a ae ‘things and 
ae ἘΠ} an 
: a ei and that thinking, e.g. a logical inference 
Θ wr 7 ν᾿ Φ . δ Cc 
“i ormally) correct when it is materially false (because - Ἔα 
1 1ἢ iss 4 Ἢ, . a als 
= e Ase But this exception in its first part cee 
Jetiti Incipii 5 
ci ae in oa Of course there are certain logical prin 
= 5 : : ic the relation of thought to thines a = ἢ 
abstr: is ia ον en 
pie : 5 er This is true of the law of Identity and C 
2 “on which requires the harmony of thoughts with = 
another TE . A On 
vic (t . ce of their agreement with actual EB 
é sit as of all other laws deri ‘ 
é erived fron 7 ae 
Logic to these portions οὐρὰ gies it. Whoever limits 
er must maintain that logical principles a 
c " } ν . . ar 
to Loei out reference to objective reality; but he wh ee 
0 ΦΦΟΘῚΟ a more comprehensiy : u u 
πλύνειν prehensive sphere will not admit tl 
maintai = - assertion in its universality Who 
aintains that ; . ı0ever 
vides laws for tl ἊΣ" does not fulfil its task unless it pro 
“age = rigid construction of the scientific te 
eig is inction from the mere general conception, for = 
al division . τ . “ir » > Natu- 
ee ‚ for the scientific form of Deduction τω : 
‘ Analocy—w ee ’ on 
Πῶς “i ee does not consider the principle f 
Ξ ) be the mere consist “4 
we ency of t nk‘ . 
with itself, but recognises truth : the thinking subject 
᾿ ἘΞ ἀκ." > O : . . 
existence, and therefore no mere e the agreement with 
necessi . 
manent in the subjective spiri ty of thought im- 
a eR ὦ e spirit, but rather a correspond 
gical with the ontological cat i Papen 
that the logical laws, havine r fe N ee 
as valid if there ge wien 2 erence to truth, would be quite 
brought forward in t} ngs nor knowledge. What is 
8 ard in the second part of the above objection ; 
ve objection is so 


' Cf. especially § 3 
: ally § 31, and the tract : 
also §§ 37, 40-44. quoted there on Idealism, &c. ; 
2 Ulrici; ef. Drobi 
; Οἱ. Drobisch, Log. 2nd ® 
Fr I ed. § 7 rd - 
p- ΧΥ11. Accordi ΔῈ] a ER ed. § 5, an 
TER ee to Drobisch, in his introduction a : a 
eae e taken from the doctrine of knowledge i ‚ only so 
get at the data for the peculiar problems ed 


far 
laws 
-- without having material truth: 


whole activ 
material truth. He who has observed all the laws of percep- 


tion and of thinking cognition in a conclusion and in the 


structur 
arrived in the conelusion (be it immediate 


Knowledge. Truth. Science. 9 











nn nn 


true that thinking may be conformable to single logical 
to single laws of Logic even as the science of knowledge 
but the agreement of the 


ity of knowledge with all these laws ensures 


e of the premisses and in the foregoing operations, has 

ly, or, as in indirect 
sroof, mediately) at material truth. The Novel does not pro- 
ceed upon (historical) knowledge, and yet must follow logical 
laws: but it must follow them only in the combination of 
antecedents with consequences. If the poet constructed his 


antecedents from the contents of perception according to logical 


as the historian and the judge do, he too would arrive 
: if he follows logical laws in the 


he thus gains for 
h itself; he 


ctive reality. The 


laws, 
throughout at material truth 


combination of antecedents and consequences, 
this combination more than mere agreement wit 


gains for it agreement with the laws of obje 
formal correctness of the mere conclusion, or generally of any 


definite part of the whole activity of knowledge, ensures 
material truth so far as it goes, 1.6. it warrants that we, so far 
as we proceed from materially true antecedents (e.g. In con- 


cluding the return of a comet or the approach of an eclipse), 


will continue in material truth, and arrive at materially true 


results. And this is just what must be expected from the view 
that logical rules rest on the principle of material truth ; while 
it does not at all agree with the opposite view, which would 
understand logical rules in abstraction from material truth. 
According to this view material truth could be ensured neither 
absolutely nor partially (e.g. from premisses to conclusion ) 
through the observance of logical rules. It must explain con- 
tinuance in truth from this stand-point—that no logical opera- 
tions carry us beyond the previously actually existing content 


of knowledge, but only raise it to fuller clearness and com- 
The fact of the enlargement of knowledge by logical 
nference (both deductive and induc- 
hich thinking follows in 


pleteness. 
combination, especially by 1 
tive), contradicts this. The rules w 








Me Ny Na Tan ED flo 
Aft » 7 m. 7 


§ 6. Place of Logic in the System of Philosophy. τι 43 


, R ; 
’ 
{ 
\ 
} 
‘ 
‘ 


10 $4. Logic as a Science. ἢ 5. Worth of Logic 











practical life and in scientific investigation ἘΠΕ ] 

comprehended and established, when Bin: advanc Bi τ 
consideration of the relation of thoucht to stielf € es = 
sideration of its relation to the objective reality he 


furthers their practical application ; it can besides (b), 
by pointing out the most-appropriate procedure, enable 
the requirements of the logical laws to be fulfilled 
under subjective limitations and hindrances. In tech- 
nical relation Logic is a mere canon and purifier of 


δὰ u: 
§ 4. The possibility of the conscious apprehension 
thought, if it be looked at only as the doctrine of the 


and sys ic r 
systematic representation of logical laws rests on 


EEE 
cir previous unconscious activity; and so Logic as 
science res 1e previ 
vei : ests on the previous exercise of the activity of 
cnowtedge. On tl 
ge. 1e othe 
ee her hand, the science of Logie 
es} oC € a conscious application of the laws of 
‚ogic and a consci IC: IV] 
nscious logical activity of thought. 
On these relati ests 
Rican se relations rests the scholastic distinction of Logica 
; ς P . . x 
pte et acquisita), Logica scholastica docens 
= — scholastica utens. Still, the name Logic stri tl ; 
aken, be - ἱ Ϊ bane 
= = i to the Logica scholastica docens, and is there. 
. ightly used in this sense chiefly by modern logici : 
= nee Θὰ ἢ ’gicians. 
peg se of logical forms and the application of Iogisa! laws 
en and must precede their theory, since the theory itself 
nly pos 
* y possible through such use; but by the ee tl ΗΝ 
ecomes more reeulat : μόδον 
, gulated and stricter istori i 
axioms upon thinking hay ee ee ee 
an ing have first of all become connected with 
oe > 
ung, and a logically regulated representation of the scienc 
es, 


and Logic itself j 
g s in gradual devel 
g velopment, does n 
| te: ot 7 
out application of these axloms ie: Ἣν 


a 2 Fi has partly an absolute, as scientifically an 
In 156 artly a r ae ἘΣ ; Ξ 

er in which ey a mer. nz <i 
and of knowi 1. En ing’ 
πλέα een 
rs exerts an influence eon thinks ἡ a of 
lally by the enunciati 1 ER en 
selves, since the a icc pri 
: aws 


agreement of thought with itself ; but it is also a canon 
and organon of knowledge, although only mediately in 
the application of its laws to a given material of know- 
ledge, if it be represented as a criterion of material 


truth. 
It is equally false to consider Logic valid only as an organon 
or canon, or mean, and only as something to be studied for 


Hegel rightly remarks, so decidedly does he 


its own sake. 
iew,! and also against 


declare both against the first one-sided v 
the second,? that whatever is in itself of the most worth, 


importance, freedom, and independence, is also the most useful, 


and that Logic forms no exception to the rule. 


ς 6, Logic is an integral part of the system 0 hilo- 
δ ὃ “ΟΣ 3 i 
sophy. Philosophy may be defined as the science of 


the universe, not according to its individual existences, 


but according to the principles which condition every 
individual, or the science of the principles of what is to 
be known in the special sciences. The principles are in 
the absolute or relative sense the first elements on 
which the series of other elements depend. In the 
svstem of Philosophy, metaphysics, including general 
rational theology (πρώτη φιλοσοφία, Arist.), makes the 
first great division, because it is the science of prin- 


ciples in general, in so far as they are common to all 


1 Wiss. der Logik, ed. 1833-84, i. 13-17. 2 Encycl. § 19. 








12 δ 6. Lhe Place of Logie in 








_. : rm . 
ge Ihe philosophy of Nature and the philoso 
) R > 1 B- F ka { 
δῷ of Spirit make the second and third divisions 
secause thev are «ci Ν 1 
ecause tney are sciences of the special principles of the 
two great spheres 

ores ıeres of existenc isting ui 
ei ἣν existence, which are distinguished 
€ opposition of impersonality or of the absence 
| elf-consciousness, and of personality or the capa 
citv for ınkı iti | = 
ty for the thinking cognition of what actually exists 
fo > 47° Ω » ; y 1 | : 
os perfection, and for ethical self-determination am 
the philosophy of Spiri | 
y of Spirit thre 
j ; e reg 
Logic, Ethics, and A Sms aa 
sie, ‚and Aesthetics, the sciences of the laws 
on t! servatic | 
2 observation of which depends the realisation 
i Ba 
the ideas of the true, the good, and tl 
ful— connect tl ce en 
= ct themselves with Psychology, the science 
O IVS + € E | 
"ἢ essential nature and natural laws of the human 

soul. E ζ Ϊ 
auth Ihe true is knowledge which agrees with what 

actually exists. The 11 Ἢ 

| y exists. The good is what corresponds to its 

inner determinati 
| ne! determination or idea, as the object of will and 

desire. T sautiful 1 
| sire. The beautiful is what corresponds to its inner 

determinati " idea, as 

mination or idea, as the object of representati 
and feeling. bie 
To these sciences is 
se sciences is further to be added, as both con 
ΒΡ ts er Α ᾿ ᾿ - 
templative and regulative, Paedagogic. or tl ' 

of training the capaciti πη 

g the capacities, determined by the genetic 
aws O ife ‘ 

is : | the mental life, to develope themselves to their 
deal ends, i.e. to the knowledge of the true, to will tl 

| ıll the 

Be and to the sense of the Beautiful; and the Philo 

so Bi » . u un > > 2 
phy οἱ History, or the science of the actual develo 

ment of the human race, in so far as it proceed ‘ 

ll see | s in 
on or disagreement with the ideal rules of d 

ve 1 > u 1 ἢ 
; Re | It includes the philosophical considerati 

[9] λιῖῶ } > 1 1 = 
the development of culture, religion. art 

‚ religion, art, and science. 


to the following remarks. 


cy 
discourse must nee 
to the definition of the notion given above, a p 


ciples can be accepted, each of which in its own series is 


the ruling one, bu 


ing upon other principles, 
higher principle from which it now derives its authority. 


this sense the common principles of all existence are to be 


the System of Philosophy. 


——— 


The complete justification of this description of the notion 


and of the division of philosophy would lead us beyond the 
bounds of this Introduction. We therefore limit ourselves here 


If we were to understand by prin- 


‚le what is thought to be absolutely without antecedent, our 
ds be of one prineiple only ; but, according 
lurality of prin- 


t when admitted into other series depend- 
can also subordinate itself to a 


In 


distinguished from the particular principles of individual 
spheres. The science which treats of the earlier evidently 
makes the first great division in any systematic arrangement. 
It bears the name of first philosophy * ever since Aristotle won 
for it an independent place, and is also called metaphysics 
after the physics in the system of the 
Aristotelian works. (This arrangement is not Aristotle’s. It 
dates from a later time, and is due probably to Andronicus 
of Rhodes; but it corresponds to Aristotle’s didactic maxim, 
that what lies nearer the senses is the earlier for us in induc- 
tive cognition, but the later in deductive cognition.) The 
divisions of philosophy which treat of the special principles of 
the individual spheres of being stand opposed to metaphysics. 
The division of these spheres into the two great groups of 
nature and of mind (Geist), of impersonal and personal exist- 
ence, does not here require vindication, as it is commonly 
It follows from this presupposition 
d the philosophy of mind 
second and third 


from its position, 


recognised by science. 
that the philosophy of nature an 
must come after metaphysics, and make the 
great divisions of the system of philosophy. The division of 
the philosophy of mind rests upon the law recognised by Aris- 
totle, that in the gradation of earthly existence every higher 


he modified character of the lower, while 


carries in itself t 
Thus, mind 


raised above it by its higher characteristics. 


1 Arist. Phys. i. 4; Metaph. iv. 3; ibid. iv. 1. 








— 


——e 


j 


=. 
—— > — 


\ 
14 §6. Place of Logic in the System of Philosophy. ὃ 





(Geist) has in itself the elements of nature and conformity 
to natural law; and the series of the branch sciences of the 
philosophy of mind begins with the science of mental life 
from the side of nature and natural law—viz. with Psy- 
chology. The personal power of self-determination, by which 
mind is raised above nature, is conditioned by the consci- 
ousness of regulative laws or laws of what should be. Since 
these laws follow from the universal demand to realise ideas 
in life, each of the three chief tendencies of the life of 
the spirit—knowledge, will, and feeling—is governed by its 
special idea. Thus arise three sciences of ruling or ideal 
laws, co-ordinate to each other—viz. the sciences of the 
laws of truth, goodness, and beauty. Lastly, since the oppo- 
sition of the laws of nature and of the regulative laws 
points towards an adjustment in which the opposites become 
one (for, under the government of the divine spirit, what 
should be and what is are one and the same), the theory of 
Paedagogic and the philosophy of history must follow psy- 
chology and the regulative sciences, and close the series of 
the branch sciences of the philosophy of mind. 

The ideas of truth and beauty stand in essentially like 
relation to the idea of moral goodness. They can and should 
all be placed in relation to the divine spirit, for all earlier 
categories are destined to return as moments in the last and 
higher sphere; but truth and beauty, as well as moral good- 
ness, must find their nearest scientific explanation from the 
essence of the finite spirit. We cannot, therefore, find (with 
Hegel) the opposition to the “ subjective spirit’ yet linked 
with nature, and running through the first course of its self- 
liberation, in the ethical relations exclusively, but must 
assion aesthetic and logic, as well as ethics, to the second 
sphere. 

The doctrine of the regulative laws of thought forms part 
of the doctrine of the regulative laws of knowledge. It has 
no claim to the rank of an independent philosophical doctrine. 


The attempt to unite the doctrine of knowledge with meta- 


physics in one and the same sclence— metaphysical or onto- 


logical logic—is untenable ; 
mental principles of any rat 
C tion wl 
acing under the same no : | 
og philosophy of spirit that philosophical science which 
0 | 


has to do with the most gen 


Study of Logie, etc. 15 


because it contradicts the funda- 


ional attempt at systematisation, by 
th one of the branch sciences 


eral principles. This come 
would vanish, if we could (as Hegel ng; ee. 0, 
edge to be the universal forms he " di Ὁ this ıs 
things in nature as well as of spiritual existences. ‘eats not 
5 ‚oceedine. Hegel’s metaphysical logic treats 
N is; Ioment and inference, but also of the analy- 
on, juc οὗ nha ᾿ 
tic a ie methods, of definition, ” = 
of construction, of proof, &e. All these .. | = eos 
‚lained as metaphysical, and, consequently; es ees ai if 
ak of spirit; but this is evidently pe pee : tial distinction 
this presupposition could be granted, the ae 5 Fe RN. 
would still exist, that those forms attain " ae 
ly to an unconscious and limited, but sag me rae: nT μὲ 
pie free conscious existence. This distinction 1s age é 
reg ween special consideration of these forms as 
nn © nn 1 in fact, with Hegel, the doctrine of the 
spirit; and, nn re in the system. It ıs = 
ne ward in Logic, in the phenomenology of reason 
μὴ ei an wat “the intelligence. Even if Hegel’s 
and in the psyc 10108 -e true (which it is not), we 
— (ῥέρμένμμα — θοροῃδ ἐν knowledge besides 
— : ον: of the two disciplines, the doctrine of = 
pig both τὰ verbal and historical grounds, has the better 
edge, 


right to the name of Logic. 


knowl 


only 


forms of ad 
notion has three differ 


$ 7. Ina system of philosophy divided page= 
purely scientific principles, Logic would = | _ vi 
first place; yet it is both lawful and suita ἢ sony 
study of Logic should precede that of the ot 1er Be er 
Ἂν as ἃ propaedeutic—lawful, for its 
hen a few universal definitions, 
able of a certain justi- 


sophical disciplines 
purposes are served W 
which are comprehensible and cap 











16 § 8. Division of Logie. 





fication outside of their own peculiar science, are taken 
out of the preceding disciplines, Metaphysics and Psy- 
chology; switable for these reasons: (a) The study of 
Logic offers less difficulty than that of those philosophical 
disciplines which go before it in scientific arrangement. 
(b) Logic makes us conscious of the methods which 
find application in itself and in the other branches of 
philosophy, and the study of Logic is a valuable exer- 
cise of thinking. In formal reference, therefore, it is 
convenient that Logic should be placed at the begin- 
ning of the whole study of philosophy. (c) The sci- 
entific representation of the system of Philosophy 
requires an introduction, in order to lead the conscious- 
ness to the stand-point of the philosophical treatment 
by means of the theory of the relations which exist 
between phenomena and Being; and the task of this 
introduction is most completely and most scientifically 
accomplished by Logic as the critical theory of knowledge. 

Hegel says, in his Letters to v. Raumer! on philosophical pro- 
paedeutic, that it has to see to the education and exercise of 
thinking. It is able to do this by removing thinking entirely 
from the region of the phantastic, by means of the determinate- 
ness of its notions and its consistent methodical procedure. 


It is able to do this in a higher measure than mathematics, 
because it has not the sensible content which mathematics has.? 


$ 8. The forms and laws of knowledge can be treated 


partly in their general character and partly in the par- 


ticular modifications which they take according to the 


1 Werke, xvii. 355. 
2(It is this thought which is the grain of truth in Sir W. Hamilton’s 
ill-judged attack on mathematics. Cf. Discussions, p. 282 ff.) 


$ 8. Division of Logic. 17 


different nature of the object-matter known ($ 2). 
The first is the problem of pure or general, the second 
that of applied or particular Logic. Pure Logic teaches 
both the laws of immediate knowledge or perception, 
and those of mediate knowledge or thought. And 
since, speaking generally, knowledge mirrors the actual 
in its forms of existence, so more particularly— 

Perception mirrors the outer order of things or their 
existence in space and time, and represents or copies 
their real motion in an ideal way ; and— 

Thought mirrors their inner order, which is the foun- 
dation of the outer. 

The forms of thought separate into as many divisions 
as there are forms of existence in which the inner order 
of things exists, and correspond to them in the follow- 
ing way :— 

Intuition or individual conception, to the objective 

individual existence ; 

Notion, with content and extent to the essence and 

“genus or species ; 

Judgment, to the fundamental relations among things; 

Inference, to the objective reign of law ; and 

System, to the objective totality of things. 


The division of Applied or Particular Logic depends 
upon the sciences to which the iogical doctrines find 
application. It treats of, for instance, the methods of 
mathematics or of the science of quantity and form, 
of the explanatory and descriptive sciences of nature, 
of the explanatory and descriptive sciences of spirit, 
and of philosophy or the science of principles. 

C 





nt a τ, ο΄. τας ποι 


——- 


18 8. Division of Logic. 








The justification of this division in its particulars, so far as 
it rests on logical principles, remains to be considered below, 
cf. §§ 36, 45, 56, 67, 74, 138; but in so far as it depends 
on metaphysical principles, cf. the first remark to § 2. 

The most common division of Logic since Kant’s time has 
been—A. General Logic: 1. Pure General Logic: a. The 
doctrine of elements; ὁ. The doctrine of method. 2. Applied 
General Logic. B. Special Logic. Comparing this with our 
division, we remark: In so far as Applied Logic is understood 
to mean the doctrine of perception and of the relation of 
thought to perception, it belongs to our Pure Logic; but in 
so far as it means the practical hints for the most suitable 
behaviour under the many subjective hindrances to thinking’ 
—[or as it is said to exhibit the laws of thought modified in 
their actual applications by certain general circumstances, 
external or internal, contingent in themselves, but by which 
human thought is always more or less influenced in its mani- 
festations 7|—it cannot be allowed to form a special division 
of Logic, because it has more a didactic than a logical charac- 
ter (cf. § 5); and Applied Logic can only be understood in the 
same sense as we speak of applied mathematics, &c., viz. the 
application of its general rules to particular wider spheres in 
which they hold good, and the consideration of the modifications 
under which they find application to each one of them. In this 
sense the notion of applied Logic does not differ from that of 
special Logic, while, on the other hand, Pure Logic is identical 
with General Logic. 

The division of Pure Logic into the doctrine of Elements and 
doctrine of Method? confuses its scientific interest with its 
didactic. Scientifically, notion, judgment, and inference are 
not merely elements of method. The notion is also an element 
in the judgment, and both are elements in inference. Besides, 
the notion, the doctrine of elements, is too relative to denote 
the opposite of Methodology. 


1 Cf. Kant, Kritik der r. Vern. Werke, ed. Hartenstein, iii. 84 ; 
Logik, viii. 18. 
2 [Hamilton, Lect. on Logie, i. 60.) ὃ [Cf. Hamilton, ibid. i. 64.] 


§ 9. History of Logic. § 10. Origin of Logic. 19 





8 9. The History of Logic has worth and meaning in 
a double relation: (a) for its own sake, inasmuch as it 
brings clearly before us the ever-ongoing struggle of 
the human mind to obtain an understanding of the laws 
of its thinking and knowing; (b.) as a mean to under- 
stand the present position of Logic, since it informs us 
of the genesis both of the parts scientifically certain, 
and of the diverse opinions prevailing at present. 

Of the works which treat of the general history of Logic, the 
most complete and thoroughgoing is the Geschichte der 
Logik im Abendlande, by C. Prantl, Ist vol. (containing the 
development of Logic among the ancients), Leipzig, 1855, 
2nd vol. (referring to the first half of the Middle Ages), do., 
1861, 3rd vol., do., 1867, and 4th vol., do., 1870 (referring to 
the latter half of the Middle Ages). 


$ 10. The foundation of Logic as a science 1s a work 
of the Greek mind, which, equally removed from the 
hardness ofthe Northern and the softness ofthe Oriental, 
harmoniously united power and impressibility. 


For its general characteristic, cf. Plato, De Republ. iv. 435 
E (ed. Steph.), and Arist. Polit. vii.7. The impressible fancy! 
of the Oriental has not the measure nor grip of strong think+ 
ing: it wants the mental power of the genuinely scientific ' 
mind. In its attempts to philosophise it is not ruled by the 
tendency to strict demonstration and to representation in a 
scientific form ; and where the art of strictly scientific thinking 
is absent, the theory can still less develope itself. Yet some 
true, deep fundamental thoughts appeared which, if they had 
been consistently followed out, would have served very well 
to be a foundation of a system of Logic. Thus the Chinese 
Meng-tse, a disciple of Kon-fu-tse, says, ‘The human mind has 
in itself the possibility of knowing all things; it must there- 
fore look to its own nature and essence, otherwise it errs. 


0% 





20 § 10. Zhe Historical: Origin of Logie. 





Only the virtuous can fathom his own essence: he who has 
fathomed his own nature can also know that of other men, he 
can fathom the essence of things.’ According to this writer 
the general original power of reason shows itself in man as the 
law of duty.! 

Among the Hindoos we find, in the philosophies of the 
Sankhya and the Nyaya, an enumeration of the kinds and 
objects of knowledge. The three ways of obtaining knowledge, 
according to the Sankhya doctrine, are, (1) Perception ; (2) Con- 
clusion (from the cause to the effect and from the effect to the 
cause, and also by analogy); and (3) Tradition (by human 
testimony and Divine revelation): the Nyaya adds Comparison. 
The Nyaya, which perhaps first arose under Greek influence, 
recognises the syllogism Nyaya (from which the system takes 
its name) in the form of five propositions, which arise out of 
the three propositions by the repetition of the minor premise 
and conclusion, according to the following-scheme :— 


Thesis—The hill is fiery. Proof— What smokes is fiery. 
Reason—For it smokes. A pplication—The hill smokes. 
Conclusion—It is fiery.” 


It is very doubtful whether the Egyptians constructed a 
logical theory. Plato praises the antiquity of their knowledge, 
but by no means the elevation of their philosophy. The Greek 
thinkers, even if acquainted with Egyptian wisdom, had to find 
out for themselves both the fundamental doctrines of Logic and 
the proofs of the elementary propositions in Geometry. 

The Greeks have undoubtedly learned much of the material 
of their knowledge from the Egyptians, and from the Orientals 
generally. The Greek mind may have needed an impulse from 
without for its development, but it owes to its own inborn in- 
dependent power, not to foreigners, what is the more essential, 
its scientific and artistic form, however actively impressible it 
may have made their treasures its own. Cf. Hegel? ‘ From 


1 Cf. Wuttke, Das Heidenthum (Breslau, 1853), ii. 102. 

2 (Cf. Colebrooke’s Misc. Essays, i. 8, and the Aphorisms of the Nyaga 
Philos., by Gautama, Allahabad, 1850. ] 

3 Philos. der Geschichte, 1837, p. 246. 


e 


Sir. Zhe Ionic Natural Philosophers, etc. 21 








what they have naturally received the Greeks have created the 
spiritual.’ The assertion of Lepsius agrees also with this:! 
< The Greeks of this great period (Thales, Pythagoras, &c.) 
collected the learning of the barbarians of all regions as ripe corn 
to the threshing-floor, to be new seed for their own fertile soil.’ 


δ 11. The speculation of the older Ionic natural philo- 
sophers (in the sixth century B.c.)—of Thales, Anaxi- 
mander, Anaximenes—was immediately directed to 
things only, not to the human knowledge of things. 
The later natural philosophers (in the fifth century ne.) 
—Heraklitus, Anaxagoras, Leukippus, and Demokritus— 
showed that sense-perceptionas such wasnot trustworthy. 
It is the reason mingled with it, and going all through it, 
which decides what truth is. Empedocles taught that 
things and man came from the same material and ideal 
elements, and that like is known by like. The Pytha- 
goreans held that the elements of number, limit and 
the limitless, are the elements of all objects. They seek 
therefore, by means of mathematical investigation and 


speculation on numbers, to get at all knowledge. Xeno- 
phanes of Colophon, the founder of the Eleatic philosophy, 
led on by his theological speculation, distinguished cer- 


tain knowledge from accidentally correct opinion. His 
immediate follower, Parmenides, the most developed of 
the Eleatic philosophers, in his polemic against the Hera- 
klitic doctrine of the universal flow of all things, and of 
the identity of contradictories, first reaches the theoretic 
consciousness of the axioms of identity and contradiction, 
although as yet in an incomplete form. Similarly, Par- 
menides taught the identity of thought with the exist- 


1 Chronologie der Aeqypter, i. 99. 





22 Sis. The Lonic Natural. Philosophers, 


ence which is thought. He set in strict opposition to 
opinion about the multiplicity and change of what exists, 
resting on the deception of the senses, the knowledge of 
the One, which is truth, able to produce conviction, and 
attained by means of thinking. His young contem- 
porary, Zeno the Eleatic, was the first to use in its 
strict form the art of managing philosophical dialogue, 
especially the art of indirect proof. Hence Aristotle 
calls him the founder of Dialectic. 


Heraklitus in Sext. Empir. adv. Math. vii. 126: Kaxoi 
μάρτυρες ἀνθρώποισιν ὀφθαλμοὶ καὶ ὦτα; βορβόρου ψυχὰς 
ἔχοντος (according to the conjecture of Jac. Bernays; com- 
monly: βαρβάρους ψυχὰς ἐχόντων). In Diog. Laert. ix. 1: 
Πολυμαθίη νόον οὐ διδάσκει". . . . ἕν τὸ σοφόν: ἐπίστασθαι 
γνώμην", ἥτε οἰακίζει (according to the conjecture of Bernays; 
commonly: ἥτε of ἐγκυβερνήσει, Schleiem. ἥτε οἴη κυβερνήσει) 
πάντα διὰ πάντων. Yet the thinking through which wisdom 
is attained is, according to the view of Heraklitus, not so 
much an activity of the mind separable from sense-perception, 
and opposed to it, but rather the sense lying open and submit-. 
ting itself to the universal all-ruling reason, while its isola- 
tion produces error.! 

Anaxagoras in Sext. Emp. adv. Math. vu. 90: ὑπὸ abav- 
ρότητος αὐτῶν (τῶν αἰσθήσεων) οὐ δυνατοί ἐσμεν κρίνειν τἀληθές. 
According to Anaxagoras,’ the divine reason knows all things, 
and the human is homogeneous with it: πάντα ἔγνω voos "---νόος 
δὲ πᾶς ὁμοῖός ἐστι καὶ ὁ μείζων καὶ ὁ ἐλάσσων. 

Demokritus, Sext. Emp. adv. Math. p. 138, informs us, divi- 
ded knowledge into what is attained through sense-perception, 
and what through the understanding. The former he calls the 
dark (oxorin), the latter the genuine (γνησίη). Demokritus 
says (p. 140) that the work of the ἔννοια is Zyrnais, the inves- 
tigation of the unknown upon the ground of the sense-phe- 


1 Cf. Sext. Emp. adv. Math. vii. 129. 
2 In Sımplie. in Arist. Phys. fol. 39 sqq. 


the Pythagoreans, and the Eleatics. 23 


nomena. Yet this thinking warrants only relatively a higher 
certainty. Man has no science in the strict sense of the 
word. Demokritus in Diog. Laért. ix. 72: ἐτεῇ δὲ οὐδὲν ἴδμεν" 
ἐν βυθῷ γὰρ ἡ anjOeva.—Empedokles in Aristot. de Anima, 1. 2: 

γαίῃ μὲν yap γαῖαν ὀπώπαμει", ὕδατι δ᾽ ὕδωρ; 

αἰθέρι δ᾽ αἰθέρα δῖον, ἀτὰρ πυρὶ πῦρ ἀΐδηλον, 

στοργῇ δὲ στοργὴν; velKos δέ τε veikei λυγρῷ. 
The doctrines of the early Pythagoreans are not accessible to us 
as they themselves represented them, since the writing ascribed 
to Philolaus,' which gave us access to many fragments, cannot 
be held to be genuine according to the investigations of 
Schaarschmidt.2 We can only trust to a sketch given by 
Aristotle.? Quotations such as the following are valuable 
only as bearing witness to the tendency of the later Pytha- 
gorean philosophy :—Pseudo-Philolaus in Stob. Eclog. i. 2, 3:4 
οὐ yap ἧς δῆλον οὐθενὶ οὐθὲν τῶν πραγμάτων; οὔτε αὐτῶν ποθ᾽ 
(πρὸς) αὑτὰ οὔτε ἄλλω ποτ᾽ ἄλλο, εἰ μὴ ἧς ἀριθμὸς καὶ a τούτω 
ἐσσία. Νῦν δὲ οὗτος κατὰ τὰν ψυχὰν ἁρμόζων αἰσθήσει πάντα 


γνωστὰ καὶ ποτάγορα (i.e. προσήγορα; corresponding to and 
connected by friendship) ἀλλάλοις ἀπεργάζεται. In Sext. 
Emp. adv. Math. vii, 92:5 ὑπὸ τοῦ ὁμοίου TO ὅμοιον KaTa- 
λαμβάνεσθαι πέφυκεν. : 
Xenophanes in Sext. Emp. adv. Math. vii. 49 ; 110; vill. 326: 


καὶ τὸ μὲν οὖν σαφὲς οὔτις ἀνὴρ ἴδεν οὐδέ τις ἔσται 
εἰδὼς, ἀμφὶ θεῶν τε καὶ ἅσσα λέγω περὶ πάντων " 
εἰ γὰρ καὶ τὰ μάλιστα τύχοι τετελεσμένον εἰπών, 
αὐτὸς ὅμως οὐκ οἶδε, δόκος δ᾽ ἐπὶ πᾶσι τέτυκται. 


Parmenides enunciates the axiom of Identity, in the meta- 
physical sense, in the words: ἔστιν or ἔστι yap εἶναι, and the 
axiom of Contradiction in the words: οὐκ ἔστι μὴ εἶναι OF 
μηδὲν δ᾽ (ἐστὶν) οὐκ εἶναι. He explains to be false the opinion 


of erring two-headed (Sixpavor) mortals, of the uncritical tribes 


1 Edited and commented on by Boeckh, Berlin, 1819. 
2 Die angebliche Schriftstellerei des Philolaus und die Bruchstücke 


der ihm zugeschriebenen Bücher, Bonn, 1864. 
3 Metaph. 1. 5. 4 See Boeckh, Philol. 141. 5 Ibid. 191, 192. 





24 §11. The Tonic Natural Philosophers, etc. 





v a . + a 
(ἄκριτα φῦλα) who hold Being and Not-Being to be identical, 
and at the same time not identical, and change every thing 
into its opposite : ὦ 

\ , A , 
ols TO πέλειν TE καὶ οὐκ εἶναι TWUTOV νενόμισται 


> > x ΄ 
κοὐ τωὐτὸν, πάντων τε παλίντροπός ἐστι κέλευθος." 


Parmenides in these verses? refers most probably to Heraklitus 
for it is Heraklitus who has enunciated this doctrine: Br 
τ᾽ ἔνι (leg. ταὐτόν ἐστι) ζῶν καὶ τεθνηκός, K.T.A., πάντα εἶναι καὶ 
μὴ εἶναι,"---παλίντονος (παλίντροποΞ) ἁρμονία κόσμου, ὅκωσπερ 
βαρ" καὶ —— He does not, however, refer to Heraklitus as 
a solitary thinker, but as a representative of the ‘ uncriti 
many, who, trusting to the Be get involved ‘a Sai 
of viewing things, full of contradictions, to which Heraklitus 
has given a philosophical form.° Since Heraklitus called the 
synthetic unity of opposites, their identity, and their existence 
in combination, a oneness of existence, he provoked that strong 
thinker, Parmenides, to the counter-assertion, and to Bite 
on the opposite extreme. Parmenides denied that true ne 
ence could have any multiplicity or any change. (This is 
the very opposition of fundamental philosophies! conception 
which appears in the Hegelian and Herbartian systems 
= re εν that the perception of Heraklitus has Bann 
absorbed in the dialectic meth 
believes that the gir eae a = ise 
ang 1e qualities 


1 Parm. Fr: 3 3 
oa m. I ragm. ed. Mullach, vv. 35, 43-51. 
= which Steinhart in the Hall. Allg. Litteraturz, 1845, p. 892 ἢ 
and Bernays in the hei n, Vil 3 1 
ays in. Museum, vii. 114 f., hav ' 
seum, Vil. „ have paid car 
attention. p = i: 
3 p mas : 
Plut. Consol. c. 10; Arist. Metaph. iv. 7, cf. iv. 8.5 
4 Plutarch, De Js Is 3 27, 3 
oh a De Is. et Os. c. 45; De An. Procr. 27, 2. 
5 So also Aristotle, De An. 1. 2 : ἐν κινήσει δ᾽ εἶ ὰ ὦ 
Pies te ” De An.i.2: ἐν κινήσει δ᾽ εἶναι ra ὄντα κἀκεῖνος 
u καὶ οἱ πολλοί, cf. Plat. Theaet. p- 179. Ina wholly analogous 
: « c 
way Herbart accuses Hegel of empiricism. . 


* Metaph. iv. 3 a es 
d ph. iv. 3, $ 14, perhaps καθά Eee 
should be read and e ἂς ny I ἘΒῈΡ TiIVEC OLOVTAL Ηράκλειτον 
Kitas II ‚and ὑπολαμβάνειν, not λέγειν, understood ; for Hera 
3 actually said that the same was and also was not (ef εἶμεν ne 
. Kat 


οὐκ εἶμεν", Her. Alleg. Hom. c. 24), but . 
.Ὁ. ὦ could ἢ °C or: 
because it was not at all Cane © AES Te ee oe 


ee 
of one thing are contradictory, bu 
of individual real essences. Herbart also attempts the pro- 


blem, not considered by Parmenides, 
the illusion of the changeable from the being of the change- 


less.) Parmenides further 


the One, to the tru 
identical with it. What exists, 


Parm. Frag. vv. 94-97 : 


12. The Sophists and Sokrates. 


t grants the multiplicity 
to derive philosophically 


teaches that thought belongs to 
ly existing, which is thought of and is 
is itself thinking, the νοῦς. 


᾽ r \ / ’ , 
δ᾽ ἐστὶ νοεῖν τε Kal οὕνεκέν ἐστι νοημῶ " 


» A 
1 @UTOV 
ἐν @ πεφατισ ένον ἐστίν 

t μ 9 


Ν La} , 
οὐ yap ἄνευ τοῦ EovTOS, 
€ 4 x a 5 Mu = \ aA Ww a v 
εὑρήσεις TO VOELV οὐδ᾽ Hv yap ἢ ἔστιν ἢ EOTAL 
» x a 9! 
ἄλλο παρεκ TOU EOVTOS. 


The deceiving senses do not judge of truth, the reason does. 


Parm. Frag. vv. 54-57: 


μηδέ σ᾽ ἔθος πολύπειρον ὁδὸν κατὰ τήνδε βιάσθω, 
νωμᾶν ἄσκοπον ὄμμα καὶ ἠχήεσσαν ἀκουὴν 
καὶ γλῶσσαν " κρῖναι δὲ λόγῳ πολύδηριν ἔλεγχον 
3 > [4 € [4 
ἐξ ἐμέθεν ῥηθέντα. 
Of Zeno the Eleatic, Diogenes Laertius informs us (ix. 25): 


φησὶ δὲ Ἀριστοτέλης ἐν τῷ Σοφιστῇ: εὑρετὴν αὐτὸν γενέσθαι διαλεκ- 
Zeno’s dialectic art consisted essentially in this, that by 


TIKENS. 
f the many ' and of motion ? he 


reasoning against the existence 0 
undertook to bring forward indirect proof for the truth of 


Parmenides’ doctrine of the One, which was genuine.? His 
dialogues appear, according to (Plato’s ?) Parmenides, p. 127, 
to have contained regular courses of reasoning (Adyous). 


$ 12. The Sophists elaborated the dialectic art, but 
often misapplied it to the purposes of subjective caprice. 
Sokrates (470-399 B.C.), who was animated by the 
idea of science, made it serve to aid the striving after that 
valid knowledge, which may be recognised by 


objectively 
ng subject to be true in the same way, and 


every thinki 


1 Simplic. in Phys. fol. 30 B. 2 Arist. Phys. vi. 9. 
3 Cf. (Plato’s?) Parmen. p. 128. 











26 13. The One-stded Sokratic Schools. 
necessarily. He sought by collecting and testing in- 
stances to recognise the general from the basis of indi- 
viduals. When he had discovered the universal, he 
endeavoured to describe it by means of the definition of 
the notion. He is therefore the founder of Induction 
and Definition, but only in their application to ethical 
problems, and apart from any logical theory. 

Protagoras ap. Diog. l. 9. 51: πάντων χρημάτων μέτρον 
ἄνθρωπος, τῶν μὲν ὄντων ws ἔστι, τῶν δὲ οὐκ ὄντων ὧς οὐκ ἔστιν. 
Ibidem: πρῶτος ἔφη δύο λόγους εἶναι περὶ παντὸς πράγματος 
ἀντικειμένους ἀλλήλοις. (Arist.?) de Melisso, Xenophane, 
Gorgia, c.5: (ὁ Topylas) οὐκ εἶναί φησιν οὐδέν" εἰ δὲ ἔστιν, ay- 
τωστον εἶναι" εἰ δὲ καὶ ἔστι καὶ γνωστὸν, ἀλλ᾽ οὐ δηλωτὸν ἄλλοι». 

Arist. Metaph. xiii. 4: δύο γάρ ἐστιν ἅ τις ἂν ἀποδοίη Ξωκρά- 
τει δικαίως, τούς τ᾽ ἐπακτικοὺς λόγους καὶ τὸ ὁρίζεσθαι καθόλου " 
ταῦτα γάρ ἐστιν ἄμφω περὶ ἀρχὴν ἐπιστήμης. Arist. Metaph. 
i. 6: Σωκράτους δὲ περὶ μὲν τὰ ἠθικὰ πραγματευομένου, περὶ δὲ 
τῆς ὅλης φύσεως οὐθέν, ἐν μέντοι τούτοις τὸ καθόλου ζητοῦντος 
καὶ περὶ ὁρισμῶν ἐπιστήσαντος πρώτου τὴν διάνοιαν." 


$ 13. Of the one-sided Sokratic Schools, the Cynic of 
Antisthenes, and the Cyrenaic or Hedonist of Aristippus, 
treat of ethical problems chiefly. Their contributions 
to Logic rest on their negative polemic against contem- 
porary systems. The NMegarie School of Euklid, and 
Eretrie School of Phaedo and Menedemus allied to it, 
mix together the principles of Sokrates and the doc- 
trines of Parmenides. Since the Megarics, in order to 
defend the unity of existence, deny the truth of sense- 
phenomena, their dialectic became gradually more and 
more a mere Eristic, which takes special delight to find 
out numerous captious and sophistical arguments. 


1 Cf. Xenoph. Memorab. iv. 5, 12; iv. 6, 1. 


14. Plato. 27. 














Antisthenes objected to the Platonic doctrine of ideas :—It 
could easily be said to what things were similar, but not what 
things were. Definitions of simple notions were ἃ useless 
waste of words (μακρὸς λόγος)" 

The Cyrenaics restricted science to the consciousness of the 
sense-affections as such; what the real object was which excited 
these, and whether it was in itself white or sweet, &e. could 
not be known.’ 

Euklid of Megara identified the One, the true existence of 
the Eleatics, with the Good of Sokrates? He vindicated his 
doctrine, as Zeno did, by indirect argument, and sought to 
show the absurd consequences which flow from the opposite 
view, which ascribes plurality and change to reality.‘ For this 
purpose his followers, Eubulides, Diodorus Reon and ane 
inus, invented a number of captious arguments ; e.8. The Liar, 
‘The Veiled,’ ‘ The Horned,’ ‘The Heap,’ and ‘ The Bald- 

head.’ al . 

The doctrine that no subject can be joined to a predicate 
which can be separated from it (e.g. man is wise), but that 
each must be predicated of itself only (e.g. man 1s man), 1s to 
be ascribed partly to the Megarics in general, but more 
especially to Stilpo, who mixed up their doctrines ΜῊΝ those of 
the Cynics,’ and also to Menedemus the Eretrian.® It 1s an 
immediate consequence from the doetrine of the oneness and 


unchangeableness of true existence. 


$ 14. Proceeding from the Sokratic method of Induc- 
tion and Definition, Plato (427-347 B.c.) developed the 


art of Logic in many ways— ae 
(a) He enriched it with the methods of Division and 


Deduction. 

1 Simplic. in Arist. Categ. fol. 54 B.; Arist. Metaph. viii. 3, cf. Plat. 
Theaet. 201, Soph. 251. 

2 Sext. Emp. adv. Math. vii. 191. 

3 Diog. Laert. ii. 106; Cie. Acad. pr. 11. 42. 

4 Diog. Laert. ii. 107. 5 Plut. adv. Col. 23. 


6 Simplie. in Phys. 20 A. 





28 δ 14. Plato. 





(b) He removed its limitation to ethical inquiry, 
and extended it to the whole sphere of philosophical 
thought. 

(c) He used it with ingenious sagacity, scientific 
exactness, care, and depth ; and still more increased the 
value of these advantages by his masterly artistic repre- 
sentation. 


Plato also developed the theory of thinking in many 
relations— 2 
(a) He surveyed the art of philosophical thinking 
in the general, and comprehended it under a nena 
notion (the notion of Dialectie). ᾿ 

(0) He strictly distinguished philosophical thinking 
not only from sense-perception, as his predecessors bad 
done, but from mathematical thinking. 

(c) He brought under observation also, and under- 
took to give an account of, the main operations of 
thought, more especially the formation of notions, De- 
finition, Division, and partly also Deduction. | 


ut Plato’s logical theorems, showing throughout 
the traces of their origin from reflection upon ideo- 
logical thinking, want both a strict separation of the 
logical from the metaphysical elements, a scientific 
completeness, and representation in a systematic form. 


If Plato’s lofty art of thinking and of representation richtl 
excites our admiration, his developments of logical theor Seis 
no less significance for the history of our science. Plato finds 
in existence the measure of thinking: Rep. v. 477 (cf. Craty] 
385 B): Adyos,—s ἂν τὰ ὄντα λέγῃ ws ἔστιν, ἀληθής, ὃς δ᾽ μὰς ἃ 
οὖκ ἔστι, ψευδής. Soph. p. 268 Β ; λέγει δὲ ὁ μὲν ἀληθὴς a τὰ 
ὄντα ὡς ἔστιν, ὁ δὲ ψευδὴς ἕτερα τῶν ὄντων, τὰ μὴ ὄντα ἄρα ὡς 
ὄντα λέγει). Plato theoretically assigns this double odie to 


§ 14. Plato. 29 





».. ...-.-:.-. 


the art of Dialectic, which he also seeks to explain in actual 
thinking—(1) to collect together into one form what appears 
scattered everywhere, in order to determine strictly each single 
one (Phaedr. p. 266, the mode of forming the notion by Abstrac- 
tion and Definition), and in this way by the same manner to 
ascend further to higher notions, until the very highest is 
reached ;! (2) then to descend again from the higher notions 
to the lower, which are subordinate to it, “to be able to distin- 
guish how each individual has grown by means of the notions of 
the kinds’ (Phaedrus, 1. i.—Division), and to examine what 
proceeds from the presuppositions laid down as a basis (Phaedon, 
101— Deduction), in order to follow it out to the last conse- 
quences. Real essences correspond to the notions, rightly 
constructed, by which they are known, the ideas, and these 
separate into the graduated series which the notions have, from 
the lower up to the absolutely highest, the idea of the Good.? 
Mathematics proceeds from postulates which are not the highest. 
Dialectic uses these said postulates as the basis on which to 
rear its ideal principles. Mathematics takes the opposite 
course, and derives from its postulates individuals and particu- 
lars. For this reason, mathematical knowledge takes a position 
between pure thought and sense-perception, and the objects of 
Mathematics are intermediate existences between ideas and 
sensible things. Since Plato distinguished in sense-knowledge 
between the trust in sense-perception and mere conjecture, and, 
in a corresponding way, in sensible objects between things 
perceived in sense and pictures or shadows, he arrives at the 


following division of ways of knowing :— 


Νόησις | Δόξα 


’ ’ > / 
ἐπιστήμη | διάνοια πίστις. | εἰκασία, 


and at the following analogous division of the whole of exist- 
ing objects :— 
Nonrov γένος ‘Opatov γένος 
/ 
ἰδέαι | μαϑηματικά σώματα | εἰκόνες 


ι De Rep. vi. 511; ef. vil. 532 8ηη. 2 Ibid. p. 509. 











30 § 15. Zhe Platonists. § 16. Arıstotle. 





It is not only characteristic of Plato’s method that he carries 
on together investigations into thinking and into what is 
thought about; it is also the peculiarity of the content of his 
doctrine that he transfers the whole relation of his forms of 
thought to the objects thought about. With him the logical 
and the metaphysical stand in a very close relation, and almost 


in immediate unity. (Yet he does not proceed to identify 
them. ) 


§ 15. Plato’s followers in the Academy felt the need 
of a stricter systematic form for the purpose of a con- 
nected exposition of doctrines. Hence Speusippus was 
induced to divide the sciences-in general, and Xenokrates 
the philosophical disciplines in particular. Xenokrates 
was the first to enunciate expressly the division of 
Philosophy into Physics, Ethics, and Dialectic. The 
second and third Academic Schools in the so-called 
Intermediate Academy, founded by Arkesilaus and Kar- 
neades, inclined to scepticism; the fourth and fifth, 
founded by Philo and Antiochus of Askalon, inclined 


to dogmatism and syncretism. 


For Speusippus s. Diog. Laért. iv. 2: οὗτος πρῶτος ἐν τοῖς 
μαθήμασιν ἐθεάσατο τὸ κοινὸν καὶ συνῳκείωσε καθόσον ἦν δυνατὸν 
ἀλλήλοις. For Xenokrates 5. Sext. Empir. adv. Math. vi. 16: 
e , Ν , > \ > ’ \ A Ν - 
ὧν δυνάμει μὲν Πλάτων ἐστὶν ἀρχηγός, περὶ πολλῶν μὲν φυσικῶν, 
περὶ πολλῶν δὲ ἠθικῶν. οὐκ ὀλίγων δὲ λογικῶν διαλεχθείς" ῥητό- 
tata δὲ οἱ περὶ τὸν Ἐξενοκράτη καὶ οἱ ἀπὸ τοῦ Ilspımarov, ἔτι δὲ 

+ 2 \ an “Ὁ ” ~ “Ὁ 7 ὯΝ 
οἱ ἀπὸ τῆς Στοᾶς ἔχονται τῆσδε τῆς διαιρέσεως. For Karneades, 
who allowed no criterion of truth, but enunciated the doctrine 
of probability, 5. Sext. Empir. adv. Math. vii. 159 sqq.; 166 
sqq. For Philo Cic. Acad. pr. ii. 6: and for Antiochus, Cic. 
ib. 1]. 6-18, 48. 


$ 16. Aristotle (384-322 B.c.) established his theory 
of Logic, as he did every branch of his system, on 


§ 16. Aristotle. I 


the foundation laid by Plato. But his pees ser- 
vice is: (a) his critical remodelling of Plato's logical 
doctrines ; (b) their development | and (ὁ) their 
systematic representation. The critical remodelling 
consists, in general, in this, that Aristotle sought to 
define more strictly the relation of the logical and meta- 
physical elements. The development belonged to every 
part of Logic; but, more especially, Aristotle created the 
theory of syllogism, which before him had scarcely ἜΝ 
worked at. The systematic division extended equally 
to the representation of the whole, and of individual 
parts. Aristotle dedicated special treatises to the whole 
of the chief parts of Logic as the nen of thinking, 
and has given a strict scientific form ® each one of 
them. For this service he has been rightly called the 
Father of Logic as a science. Aristotle collects together 
the most important part of his logical investigations— 
the doctrine of inference and proof—under the title 
Analytic, because the logical structure of thought 1s 
here as it were analysed, 1.6. separated and reduced to 
ἕως elements. He does.not give one common name to 
all the parts. His successors and commentators ae 
his collected logical writings the Organon. Dialectic 
with Aristotle is the art of the critical ἐξέτασις of a thesis, 
or proceeding from propositions which are held = = 
true, but are doubtful, to derive conclusions, τς δὶ en 
get at some decision upon their truth or ΓΙ τῶν : = 
propositions τ deals with are mainly pro ab e τ 05 ) 
Logical means with Aristotle the panniers : be 
general notions (λόγοις); after the manner Οἵ ἡ go> : 
and Plato, in opposition to physical treatment, which 























( 


\ 


32 δ 16. Aristotle. 





has to do with the specific and individual qualities. 
The science which is represented in the Organon was 
called Logic by the Stoics and by some of the commen- 
tators of Aristotle. | 


The Aristotelian remodelling of the Platonic doctrines can- 
not be understood, although modern writers have often so mis- 
understood it, in the sense that Aristotle considered the form of 
thought without any reference to objective reality. The stand- 
point of the Aristotelian is by no means identical with that of 
the modern Subjective-formal Logic. This has been proved by 
Ritter,! Trendelenburg,? Zeller,? Bonitz,* Brandis® (although 
he accepts an essential relationship between the Aristotelian and 
the modern Formal Logic), and by Prantl.6 Aristotle finds 
the standard of truth, as Plato had, in the agreement of thought 
with what actually exists, which is the limit of science.’ The 
notion, rightly formed, corresponds, according to Aristotle, to 
the essence of the thing (οὐσία or τὸ τί ἣν εἶναι, cf. § 56); the 
judgment is an assertion about an existence or a non-exist- 
ence; affirmation and negation correspond to union and sepa- 
ration in things; the different forms which the notions take in 
the judgment (or the kinds of denotation of existences, σχή- 
ματα τῆς κατηγορίας τῶν ὄντων) determine themselves according 
to the forms of existence; the middle term in a syllogism 
correctly constructed corresponds to the cause in the connected 
series of real events; the principles of scientific knowledge 

orrespond to what is actually the first in the nature of things. 

Aristotle gives to the whole of his logical investigations the 


1 In his Geschichte der Philos. iii. 117 ff. 1881. 

2 In his Logischen Untersuchungen, 1st ed. 18-21, 1840 ; 2nd and 3rd 
ed. 30-33, 1862, 1870; cf. Elem. log. Arist. 6th ed. 1868, ad § 63. 

3 Philos. der Griechen, ii. 373 ff., 1846; 2nd ed. ii. 2, 131 ff., 1860. 

4 Commentar zur Arist. Metaph. 187, 1849. 

5 Gesch. der Gr.-R. Phil. ii. 2nd ed. 371 ff.; 432 ff., 1853. 

6 Gesch. der Logik, i. 87 ff.; 104 ff.; 135, 1855. 

7 Metaph. iv. 7; ix. 10; x. 6; cf. Categ. 12, 14 8. 21: τῷ yap 
εἶναι TO πρᾶγμα ἣ μὴ ἀληθὴς ὁ λόγος ἢ ψευδὴς λέγεται. 


« 


§ 16. Aristotle. 33 


name Analytic (τὰ avaduTixa), 1.€. the analysis of thought (not 
the doctrine of merely analytic thinking), and desires that 
every one will first make himself familiar with it before he 
proceeds to study the First Philosophy or Metaphysie.! 

With regard to the single logical writings, the book De 
Categoriis, περὶ κατηγοριῶν (whose authenticity is not quite 
undoubted ; perhaps caps. x.-xv. have been inserted by a 
stranger), treats of the forms of notions and of the corre- 
sponding forms of existence. The book De Interpretatione, 
περὶ ἑρμηνείας (whose authenticity was doubted by Andronikus 
of Rhodes), treats of the proposition and judgment. The two 
books Analytica Priora, ἀναλυτικὰ πρότερα, treat of inference. 
The two books Analytica Posteriora, ἀναλυτικὰ ὕστερα: 
treat of proof, definition and division, and the knowledge of 
principles. The eight books of the Topica, τοπικά, treat of 
dialectical or probable inferences. Lastly, the book De 
Elenchis Sophisticis, περὶ σοφιστικῶν ἐλέγχων, treats of the 
deceptive inferences of the Sophists and of their solution. The 
best new collected edition of these writings is Aristotelis 
Organon, ed. Theod. Waitz.2 Trendelenburg’s Elementa Lo- 
gices Aristoteleae is a very good help to the study of the 
chief doctrines of Aristotles Organon.? For a wider and 
more thorough-going acquaintance, the student may be 
referred to the well-known historical work of Prantl, Ge- 
schichte der Logik, and more especially to the representation 
of the Aristotelian philosophy given by Brandis in his 
Handbuch der Geschichte der Griech.-Röm. Philos. ii., 2nd 
pt., 1853. Biese (Die Philosophie des Arist. Logik und 
Metaphysik, 1835) may also be consulted. For the meaning 
of the expressions Analytic and Dialectic in Aristotle, see 
Trendelenburg, Elem. Arist., Int. and § 33; and Charles 
Thurot, Ktudes sur Aristote, Paris, 1860, p. 118 ff For 
the meaning of Aoyınos, see Waitz ad Organon Arist. 82 B, 35; 
Schwegler ad Arist. Metaph. vii. 4; xi. 10; Prantl, Ge- 
schichte der Logik, i. 535 f. Aristotle refers the Λογικῶς 


1 Metaph. iv. 3; vii. 12. 2 Lips. 1844-46. 
3 Berol. 1836, Sth ed. 1862. 
D 











34 § 17. The Peripatetus. 











Ζητεῖν (in opposition to the φυσικὴ oxeyrus) more particularly to 
Plato and the Platonists,! partly with recognition of the 
superiority of their investigation into notions,’ partly and 
chiefly blaming them, because the merely logical treatment, 
the more it proceeds upon the general notion, the further it 
is from the particular qualities. He says:° λέγω δὲ λογικὴν 
(τὴν ἀπόδειξιν) διὰ τοῦτο; ὅτι ὅσῳ καθόλου μᾶλλον, ποῤῥωτέρω 
τῶν οἰκείων ἐστὶν ἀρχῶν. In the time of Cicero Aoyımn 
was in common use to denote the doctrine of knowledge 
and representation (especially whilst the influence of the 
Stoics lasted). He says, e.g. De Fin. 1. 7: in altera philo- 
sophiae parte, quae est quaerendi ac disserendi, quae Λογική 
dicitur. The expression ἡ λογικὴ πραγματεία 1s common 
with Alexander of Aphrodisia, the Interpreter of Aris- 
totle. Boethius says: logicen Peripatetici veteres appella- 
verunt. Seneca and Quintilian use the expression, rationalis 
philosophia, rationalis pars philosophiae. Thomas of Aquino 
rightly explains the sense of this in his Commentary on 
Arist. Anal. Post.: Ratio de suo actu ratiocinari potest— 
et haec est ars logica, 1.6. rationalis scientia, quae non solum 
rationalis ex hoc, quod est secundum rationem, quod est omni- 
bus artibus commune, sed etiam in hoc, quod est circa ipsam 
artem rationis sicut circa propriam materiam. Cf. Kant,' 
who says, ‘that it (Logic) is a science of the reason, not of 
its forms merely, but also of its matter, since its rules cannot 
be derived apart from experience, and since it has at the same 
time reason for its object.’ 


$ 17. The carlier Peripatetics, giving their atten- 
tion to empirical investigation, developed the Logic of 
Aristotle in a few particulars only. The later Peri- 
patetics restricted themselves to the task of advancing 
the study of Aristotle’s labours by commentaries. 


I Metaph. xii. 1, and elsewhere. 2 Thid. xiii. 5. 
3 De Generat. Animal. ii. 8, p. 747 B, 28. 


4 Logik, Werke, viii. 14, Harten. ed. Leip. 1868. 


§ 18. The Epikureans, Stoics, and Skeptics. 35 





Theophrastus and Eudemus established the theory of Hypo- 
thetical and Disjunctive Inference. They developed the theory 
of the Categorical Syllogism by adding five new ones, moods 
of the first figure, to the fourteen Aristotelian moods. The 
so-called Fourth Figure was afterwards constructed out of 
these. For the particulars, see § 103. Of the Later Peripa- 
tetics, the most prominent were Andronikus of Rhodes, who 
classified the works of Aristotle, and Alexander of Aphrodisias, 
the Interpreter. The labours of Galen and of the Neo- 
Platonists are to be added to theirs. See Brandis upon the 
Greek expounders of the Organon of Aristotle in the Proceed- 
ings of the Berlin Academy of Sciences, 1833. 


$ 18. Epikurus (341-270 8.0.) lowers the value of 
Logic, which he calls Canonic. He places it exclusively 
at the service of his Hedonist Ethics, passes over the 
harder doctrines, and makes sense-perception and the 
conception proceeding from it the final judge of truth. 

The Stoics, whose mode of thought owed its origin 
to Zeno of Cittium (circa 300 B.c.), and was built up 
into a system by Chrysippus (282-209 B.c.) chiefly, 
developed the Aristotelian doctrine of thought in parti- 
cular parts, by their elaboration of the doctrine of the 
hypothetical and disjunctive syllogism, and added to it 
the beginnings of a theory of perception and of its 
value for knowledge. From their investigations into 
the criterion of truth, their Logic, more distinctly than 
Aristotle’s, acquired the character of a theory of know- 
ledge. They attribute to sense-perception, and in a 
higher degree to thinking, the capacity to become a 
true picture of actual existence. Some of the Stoics 
comprehended, under the name Logic, dialectical doc- 
trines (i.e. those of the theory of thinking and know- 


ing) and those of grammar and rhetoric. 
ῃ 2 

















ei =e se 
ge nn — 


¥ 
TS 





a BREE EEE ng an σαν 


Pr -- 
> nn 




















18. The Epikureans, Stoics, and Skeptics. 


The Skeptics combated dogmatism in general, and 
especially that of the Stoics. The chief representatives 
of Skepticism are the followers of Pyrrho of Elis (circa 
320 2.c.), and the Philosophers of the Intermediate 
Academy. 


For Epikurus see Diog. Laert. x. 31: ἐν τοίνυν τῷ Κανόνι 
λέγει ὁ ᾿Επίκουρος, κριτήρια τῆς ἀληθείας εἶναι τὰς αἰσθήσεις καὶ 
προλήψεις καὶ τὰ πάθη. Cicero!: tollit definitiones, nihil de 
dividendo ac partiendo docet; non quo modo efficiatur con- 
cludaturque ratio tradit; non qua via captiosa solvantur, 
ambigua distinguantur ostendit; iudicia rerum in sensibus 
ponit.? Some later Epikureans, Zeno (circa 100 8.0.) and his 
scholar Philodemus, following in the steps of Epikurus, have 
treated of the mode of concluding from signs (σημεῖα, σημει- 
ova bat). | 

For the Stoical division of Logic see Diog. Laert. vii. 41: 70 δὲ 
λογικὸν μέρος φασὶν ἔνιοι eis δύο διαιρεῖσθαι ἐπιστήμας, εἰς ῥητορ- 
ικὴν καὶ εἰς διαλεκτικήν, οἵ. Senec. Ep. 89; upon the φαντασία 
καταληπτική and the mpoAmYıs issuing from it, Diog. L. vil. 46 ; 
Cie. Acad. Post. i. 11: visis non omnibus adiungebant fidem, 
sed iis solum, quae propriam quandam haberent declarationem 
earum rerum, quae viderentur—unde postea notiones rerum 
in animis imprimerentur.—Stob. Eclog. Eth. ἢ. 128: εἶναι δὲ 
τὴν ἐπιστήμην κατάληψιν ἀσφαλῆ καὶ ἀμετάπτωτον ὑπὸ λόγου. 

The Skeptics find no sure ground for distinguishing between 
two opposite opinions either in perception or in the notion, 
and therefore limit themselves to the acceptance of the phe- 
nomena as such, abstaining (ἐποχή) from any judgment upon 
their objective truth.” The grounds of doubt which, accord- 
ing to Aristokles,* seem to have been collected by Aenesidemus 
are quoted by Sext. Emp.” They rest chiefly upon subject- 
ive differences conditioned by the relativity of conceptions. 
Sextus, a physician of the Empirical School, gives a very 

ı De Fin. i. 7. 2 Cf ib. ii. 6. 3 Diog. Laert. ix. 103 sqq. 

4 Ap. Euseb. praepar. Evang. xiv. 18. 

5 Hypotyp. Pyrrhon. i. 36 sqq, ; Diog. Laert. ix. 79 sqq. 


δ 19. Neo-Platonists. § 20. Christian Fathers, etc. 37 











copious collection of the whole of the Skeptical arguments of 
antiquity in his two works which are extant: Πυῤῥωνείων 
ὑποτυπώσεων βιβλία τρία and Ipods μαθηματικοὺς βιβλία ἕνδεκα. 


§ 19. The Neo-Platonists (whose mode of thought 
appeared in the third century A.D.), inclining to meta- 
physical-theosophic speculations, placed the ecstatic in- 
tuition of the divine high above scientifically elaborated 
knowledge. They diligently studied the logical inves- 
tigations of Plato and Aristotle, without essentially 
advancing them in an independent way. 


Plotinus (204-269 A.D.) tried to remodel the Aristotelian 
doctrine of the Categories; the later Neo-Platonists went 
back to it. Porphyry (232-304 A.D.), scholar of Plotinus, 
was the author of the introduction to the Organon of 
Aristotle, so much read in the Middle Ages. It treats of the 
logical notions of Genus, Species, Difference, Property, and 
Accident. Their numerous commentaries upon the writings 
of Plato and Aristotle, in part still extant, evidence the 
studies of the Neo-Platonists. 


§ 20. The Philosophy of the Church Fathers is essen- 


tially a philosophy of religion, and, grappling with the 


difficulty of the problems nearest it, takes only a secon- 
dary interest in the problems of Logic. The Platonic 
doctrine of ideas attracted their attention, but in a sense 
which departs essentially from the original one. Au- 
gustine, following Plotinus, makes the idea immanent 
in the divine mind. The chief doctrines of the Aris- 
totelian organon were incorporated in the text-books of 
the so-called seven liberal arts, and thus became an 
object of instruction in the Christian Schools from the 
sixth century. The Organon, as well as the Aristotelian 

















a1. The Schoolmen. 





works generally, was also diligently studied by the 


Arabian and Jewish literati. 
The relation of the Church Fathers to Greek Philosophy is 


a various one. Justin Martyr (cire. 150 A.D.) thus asserts his 
conviction : of μετὰ Λόγου βιώσαντες Χριστιανοί εἰσι; κἂν ἄθεοι 
ἐνομίσθησαν, οἷον ἐν “Ἕλλησι μὲν Σωκράτης καὶ Ἡράκλειτος 
καὶ οἱ ὅμοιοι avrois.! Clement of Alexandria, Origen, and 
others are friends of the Greek Philosophy, and place it at the 
service of Christian Theology. Others, as Irenaeus, his dis- 
ciple Hippolytus, and Tertullian, frightened by the Gnostic 
Syncretism, were afraid of danger from it to Christian doc- 
trine. Others, again, such as Augustine (354-430), keep 
a middle course. The contact with Neo-Platonism was partly 
friendly, partly antagonistic. Augustine grounded the truth 
of knowledge in general on the truth of the knowledge of 
our inner life (cf. §40). Ideas are for him: principales formae 
quaedam vel rationes rerum stabiles atque incommutabiles, 
quae in divina intelligentia continentur.? Boéthius (470-525 ) 
translated and commented on several treatises of Aristotle’s 
Organon, and explained the Introduction of Porphyry. 
Marcianus Capella (cire. 430) and Cassiodorus (cire. 500), 
in their text-books of the seven liberal Arts (Grammar, Rhe- 
toric, Dialectic, Arithmetic, Geometry, Astronomy, and 
Music), treat, among others, of Dialectic or Logic, following 
the course of Aristotle. Isedorus Hispalensis (circ. 600), 
Bede (cire. 700), Aleuin (736-804), follow in their footsteps. 
Among the Arabian Aristotelians, Avicenna (Ibn Sina, cire. 
1000 A.p.) and Averroés (Ibn Roschd, circ. 1175) were 
specially famed. ὙΠῸ most noted of the J ewish Aristotelians 
was the contemporary of Averroés, Moses Maionides (Moses 
Ben Maimun, 1135-1204), ‘ the light of the Jews of the 


Middle Ages.’ 

§ 21. In the Middle Ages the Scholastic Philosophy 
developed itself partly under the influence of the 
Church Fathers, partly under that of the logical writ- 


1 Justin. Apolog. i. 46, 88 c. 2 De Div. qu. 46. 


21. The Schoolmen. 39 





ings of Aristotle, and later (about the beginning of the 
thirteenth century) under that of his other works. 
The essential characteristic of the Scholasticism of the 
Middle Ages is the application of the understanding, 
arranging and inferring, to the formal outside of dog- 
matic, and of sciences whose contents have been tra- 
ditionally given. It has significance for Logic in a 
double reference: (a) by its subtle extensions of the 
Aristotelian Syllogistic; and (b) by the struggle of 
Realism with Nominalism in the question about the 
real existence of universals. Realism acquired an 
almost unlimited sovereignty in the bloom-time of 
Scholasticism ; Nominalism, asserting that the uni- 
versal was not something real, but only existed in the 
word, or at least in the conception (conceptualism), and 
thereby threatening to lower the value of Scholastic 
Art, appeared in the beginning of Scholasticism only 
in an isolated and transitory way, and in its last period 
more generally and victoriously. 


The universal tendency of Scholasticism is summed up 
in the maxim of Anselm of Canterbury (1033-1109), “ credo 
ut intelligam.’ As was natural, this striving after a scientific 
rational insight, when it first came into power, busied itself 
with a formal systematising of the given contents of the doc- 
trines of faith and of the sciences. The knowledge of the 
logical works of Aristotle was, until the time of Abelard 
(1079-1142 A.D.), limited to the Categories and the De 
Interpretatione, along with the Isagoge of Porphyry. The 
contents of the other parts of the Organon were known 
through the text-books of Boéthius, the Principia Dialect. 
of Augustine, and the pseudo-Augustinian treatise on the 
ten Categories.’ Soon after, about the middle, and even 


I According to the testimony of Abelard in Cousin, Oeuvres ined. 











40 S21. The Schoolmen. 








before the middle, of the twelfth century, the knowledge 
of both Analyties, of the Topics, and of the Soph. Elench. 
had gradually diffused itself, partly in the translations of 
Boéthius, partl¥ in other new and more literal translations. 
John of Salisbury (d. 1180, Bishop of Chartres) knew the 
whole Organon. Partly perhaps in the course of the twelfth 
century, partly in the beginning of the thirteenth, Logic 
received an addition, which consisted essentially in the re- 
ception of grammatico-logical notions and doctrines. These 
new forms were made popular by the Compendium of Petrus 
Hispanus (d. 1277, Pope John XXI), the Summulae 
Logicales, in which, among other things, the mnemonic words 
for the forms of the Syllogism are found. The logical 
doctrines were here expounded in six parts (tractatus) ; the 
first of which gives a summary of the contents of the book De 
Interpretatione. The second treats of the ‘ quinque voces ’ 
of Porpyhry—Genus, Species, Difference, Property, and 
Accident; the third, of the Categories; the fourth of the 
Syllogism ; the fifth, of the Topics; the sixth, of the Soph. 
Elench. A seventh part treats of De Terminorum Proprieta- 
tibus. It speaks of the use of substantives, and especially of 
their ‘ suppositio,’ i.e. the representation of the more special 
by the more general, of proper nouns by common nouns, also 
of adjectives and verbs, and of the ‘ syncategoremata,’ 1.6. 
the other several parts of speech. This seventh part is also 
called the Parva Logicalia, and is often published sepa- 
rately under this title. The part of the Aristotelian Logic 
which was the earlier known was called the Vetus Logica, 
and the part which became known about 1140, the Nova 
Logica. The representatives of Logic extended by the doc- 
trine ‘de term. prop.’ were called “ Moderni,’ and the corre- 
sponding parts of the whole of Logic, ‘ Tractatus Modern- 
orum.’ Occam, the reviver of Nominalism (circ. 1320), has 
‘woven into the whole doctrine of Universals’ the pro- 


p. 228, cf. Prantl, Gesch. der Logik, ii. 100. Besides this, Abelard 
perhaps knew indirectly single sentences which Aristotle had enunciated 
in other logical treatises. 


§ 22. Earlier Times of the Reformation. 41 





positions and terms of this part of Logic.’ It is better not to 
assume (as Prantl does) that this ‘ Modern Logic’ rests on a 
Byzantian influence. A Greek compend, which contains 
these additions, and quite in the same way as the Summulae 
of Hispanus, has been ascribed by some to Michael Psellus, 
who lived in the eleventh century. If this be true, it must 
have been copied by Hispanus and other later Logicians, but 
it is more correctly believed to be a translation of the text- 
book of Petrus Hispanus. The metaphysical and physical 
writings of Aristotle ? were known in the West since the end 
of the twelfth and beginning of the thirteenth centuries ; for 
the Arabian and Hebrew translations were then translated into 
Latin. Soon after, also, the Greek texts were obtained from 
Constantinople, when once the taking of that city by the 
Crusaders (1204) had opened up this way. 

Realism had among its followers Anselm, Albertus Magnus, 
Thomas of Aquino, Duns Scotus; to Nominalism belonged 
Roscellinus, and also Abelard (with an approach to Conceptual- 
ism); and later, after the fourteenth century, William of 
Occam, Buridan, Peter of Ailly, Biel, and others. Melanch- 
thon was also a Nominalist. The chiefs of Scholasticism 
themselves, Albertus Magnus (1193-1280), Thomas of Aguino 
(1225-1274), and Duns Scotus (d. 1308), did not disdain to 
write commentaries on the logical writings of Aristotle. 

Of the fantastic ‘ ars magna et ultima’ of Raymond Lully 
(1234-1315), a kind of combining topic, Des Cartes rightly 
judged when he said,? that it served only ‘ad copiose et sine 
iudieio de iis, quae nescimus garriendum.’ 


$ 22. The revival of the study of the old classical 
literature, and the great struggle for the reformation of 
the Church, made the questions disputed by Scholastics 


1 According to Prantl, Sitzungsber. der Münchener Akad. 1864, 
ii. 1, p. 65. Cf. Geschichte der Log. iii. 334 ff. 

2 Cf A. Jourdain, Recherches crit. sur l’äge et l’origine des Trad. 
iat. d’Aristote, Paris, 1819, 2nd ed. 1843. 

3 Disc. de Methodo, ii. 


























42 § 23. Bacon of Verulam. 





lose all their interest. Yet in the universal break with 
traditionalism lay the germ of a new independent 
development of Logic, as well as of Philosophy in 
general. The study of Logic was retained and ad- 
vanced by the reformers. Text-books written by 
Melanchthon, and based upon the works of Aristotle, 
long served in Protestant schools to give the elements 
of logical instruction. Aamus stood forth as the op- 
ponent not only of Scholastic but of Aristotelian Logic. 


Among the classically trained men of the time, Laurentius 
Valla (1415-1465), Agricola (1442-1485), and Ludovicus 
Vives (1492-1540) helped to purify Logic from Scholastic 
subtlety. Melanchthon (1497-1 560) in his treatises— Dialectica, 
1520; Erotemata Dialectices, 1547—placed the didactic side 
of Logic in the foreground, for he explained Dialectic to be 
the “ars et via docendi.’ His example and precept, * carere 
monumentis Aristotelis non possumus,’ restored again amongst 
Protestants the authority of Aristotle, which the assaults of 
Luther had at first threatened to overthrow. 

Peter Ramus (Pierre de la Ramée, 1515-1572)—in his Dia- 
lecticae Partitiones, 1543; Institutiones Dialect., 1547 ; Scholae 
Dialect., 1548—has done more to agitate than to positively 
advance the science. The like may be said of the tumultuous 
endeavours of the contemporary Natural Philosophers of Italy 
—Telesius, Campanella, Bruno, and Vanini, and also of the 
Natural Philosopher and physician Paracelsus, and others— 
who have, with all their fancifulness, done a lasting service, 
inasmuch as they founded their doctrine of nature, and their 
view of the universe, upon observation and mathematics. By 
his maxim ‘ to begin from experience, and by means of it to 
direct the reason,’ Leonardo da Vinci (1452-1519) became 
a predecessor of Bacon. 


§ 23. Bacon of Verulam (1561-1626), a champion 
of the anti-scholastic tendency of his time spending it- 





§ 23. Bacon of Verulam. 43 


self on the investigation of Nature, brings into Logic 


an essentially new element by his theory of inductive 
knowledge. He wished Induction to ascend from the 
‘ndividuals which are the objects of experience, first to 
notions and propositions of intermediate universality, 
then by degrees to knowledge of higher universality. 
Bacon holds that the syllogism is not valid as a means 
of scientific investigation, because it does not lead to 
principles, and in the descents from principles cannot 
increase the subtlety of Nature, and that it is only 
suitable for disputations. Bacon undervalued the 
worth of the deduction of the particular from the 
general, and the significance which the syllogism has 
for deductive and mediate, and also for inductive know- 


ledge. 


Bacon has stated his opinions in his treatise De Dignitate 
et Augmentis Scientiarum, and in the Novum Organum. He 
says:! Scientia nihil aliud est, quam veritatis imago; nam 
veritas essendi et veritas cognoscendi idem sunt, nec plus a se 
invicem differunt, quam radius directus et radius reflexus.’— 
Syllogismus ad principia scientiarum non adhibetur, ad media 
axiomata frustra adhibetur, quum sit subtilitati naturae longe 
impar. Assensum igitur constringit, non res.’— Sy llogismus ex 
propositionibus constat, propositiones e verbis, verba notionum 
tesserae sunt. Itaque si notiones ipsae, id quod basis rei est, 
confusae sint et temere a rebus abstractae, nihil in 115 quae su- 
perstruuntur est firmitudinis. Itaque spes una est in induc- 
tione vera. According to the Nov. Org.;' Inductive Logic 
is not, like the common Logic, to be a standard for an intel- 
lectual activity only abiding in itself, but is to bea standard 
for the knowledge of things: ita mentem regimus, ut ad rerum 


2 Novum Org. i. aphor. xill. 
4 Ibid. i. 127. 


1 De Augm. i. 18. 


3 Ibid. xiv. 



































44 § 24. Des Cartes. 








naturam se applicare possit. This Logic boasts itself to be a 
key to every science, since it directs and .strengthens the 
thinking mind in its striving after knowledge:! Rationales 
scientiae reliquarum omnino claves sunt; atque quemad- 
modum manus instrumentum instrumentorum, anima forma 
formarum, ita et illae artes artium ponendae sunt. Neque 
solum dirigunt, sed et roborant, sicut sagittandi usus non 
tantum facit, ut melius quis collineet, sed ut arcum tendat 
fortiorem. In the Nov. Org.? Bacon asserts that his induc- 
tive method is applicable to the intellectual and moral sciences, 
but does not proceed to apply it. This application was only ‘a 
dark presentiment from afar ’ (Beneke). Bacon has seldom 
given the correct methods of investigation in particular cases, 
still seldomer reached good scientific results in his investiga- 
tions, and has not even recognised as valuable nor appropriated 
the best of the discoveries already made in his day by others 
(all which Zasson and Liebig have made manifest, while they 
were opposing the previously very widely-extended over- 
estimation of Bacon); but he did this service, he more 
strongly opposed than any of his predecessors the trivialities 
of Scholasticism, he firmly established universal laws of in- 
ductive investigation, and he gave a place in Logic to the 
new tendency, with its methods and principles. Cf. § 134, on 
Hypothesis and the ‘ Experimentum crucis.’ 


$ 24. If Bacon paid almost exclusive attention to 


sense-perception and outer nature, Des Cartes (1596- 
1650), on the other hand, found in the inherent certainty 
of the thought of his own existence the one starting- 
point of philosophical knowledge which could with- 
stand every doubt. He made the subjective clearness 
and distinctness the criterion of objective truth, and 
found security for the validity of this criterion in the 
divine truthfulness, which could not allow a clear and 


1 De Augm. v. 1. 2 Ibid. i. 127. 





§ 24. Des Cartes. 45 


distinct conception to be a deceptive one. Des Cartes 
accordingly believes that by means of this critcrion the 
human mind can truly know both its own thinking in 
the widest sense of the word, or its whole inner conscious 
activity, the divine nature, and, as the properties of 
extended things, extension in space and its modes. He 
calls immediate knowledge Intuition ; every mediate 
way of knowledge he comprehends under the general 
notion of Deduction. In mediate knowledge Des Cartes 
occasionally distinguishes a double method of exhibiting 
his fundamental doctrines—the analytic and the syn- 
thetic: the former, which proceeds from what is imme- 
diately given to principles, serves for discovery ; the 
latter, which proceeding from principles deduces single 
theorems, serves for strict demonstration. 

Des Cartes believes that in four general directions he 
exhausts all that can be said about method. The first 
rule demands evidence which is founded on perfect 
clearness; the second, a division of the difficulties ; the 
third, an orderly; and the fourth, a continuous advance 
in investigation. Every error is due to an abuse of 
the freedom of the will, leading to hasty judgment. 

Des Cartes enunciates! the following definition of Clear- 
ness and Distinctness:—Claram voco illam perceptionem, 
quae menti attendenti praesens et aperta est, distinctam 
autem illam, quae quum clara sit, ab omnibus aliis ita 
seiuncta est et praecisa, ut nihil plane aliud, quam quod 
clarum est, in se contineat. The four rules of method (which 
are not so much logical laws as rules, which we must 


receive subjectively in order to be able to comply with the 
logical standard, and so escape errors) are to be found in 


1 Princip. Phil. 1. § 45. 





= = = = ae = —— 
SES ES m Ὁ = τ So 
υ — ge rn > _ = ~ 

















46 § 24. Des Cartes. 





Discours de la Méthode pour bien conduire sa raison et chercher 
la vérité dans les Sciences, 1637,' sec. part. Des Cartes says: 
‘Thus, instead of the great number of precepts of which Logic 
is made up, I thought that the four following would be suf- 
ficient, provided I firmly and constantly resolved not to fail 
even once in observing them.. The first was, never to accept 
anything as true, unless I recognised it to be so evidently, i.e. 
to avoid carefully haste and anticipation, and to include nothing 
in my judgments but what should present itself so clearly and 
distinctly to my mind that I should have no occasion to doubt 
it. The second was, to divide each of the difficulties I had to 
examine into as many parts as would be requisite for better 
resolving them. The third was to arrange my thoughts in an 
orderly fashion, beginning with the most simple objects, and 
those most easily understood, to ascend little by little, by 
degrees as it were, up to the knowledge of the most compound, 
and to imagine an order even between those which do not pre- 
cede each other naturally. And the last was, to make every- 
where such complete enunciations and such general reviews, 
that I should be certain I had omitted nothing.’ In the same 
place, Des Cartes says of the Syllogism, and of most of the 
other doctrines of Logic, that they have more a didactic than a 
scientific value: ‘ As for Logic, its syllogisms and the majority 
of its other precepts are of avail rather in the communication 
of what we already know than in the investigation of the 
unknown.’ Des Cartes touches upon the distinction between 
Analytic and Synthetic methods in his replies to objections 
against his Meditationes de Prima Philosophia, Respons. ad 
secund. obiect. Inthe treatise, Regulae ad Directionem Ingenii 
(first published in his Opuscula Posthuma, Amstelod. 1701), 
Des Cartes distinguishes Intuition, or Knowledge immediately 
certain, by which we become conscious of principles, and 
Deduction, or the operation by which we deduce a knowledge, 
which is the necessary consequent of an other, and recog- 
nise it because of the other. The demands contained in the 


1 Diseursus de Methodo recte utendi Ratione, 1644. [Translated 
into English by Prof. Veitch, p. 61, Edin. 1863. | 





§ 25. Spznoza. 47 








four directions for method in the Discours are further deve- 
loped by Des Cartes into rules when he applies them to single 
philosophical, and especially mathematical, problems. The 
most celebrated logical work which has proceeded from the 
School of Des Cartes is La Logique, ou art de penser, Paris, 
1662,' in which the doctrines of Aristotle are combined with 
the principles of Des Cartes. It defines Logic to be the art 
of the right use of reason in the knowledge of things (l’art 
de bien conduire sa raison dans la connaissance des choses, tant 
pour s’instruire soi-m&me que pour en instruire les autres). 
This work is probably due to Antony Arnauld, assisted by 
Nicole and other Jansenists of the Port-Royal. 

Nicole Malebranche (1638-1715), the representative of the 
doctrine that we see all things in God, in his work, De la 
Recherche de la Vérité, Paris, 1673, proceeds upon the funda- 
mental principles of Des Cartes. 

Among the opponents of Des Cartes, Gassendi (1592-1655) 
deserves special mention for his clear and well-arranged repre- 
sentation of Logic. 


§ 25. Spinoza (1632-1677) traced false or inadequate 
knowledge to the influence of the imagination, true or 
adequate knowledge to thought. Truth is the agree- 
ment of the idea with its object. Truth makes clear 


both itself and error. The intuitive understanding 


recognises each individual from its causes, and the finite 
generally from the infinite. It attends, in the first 
place, to the idea of one substance whose essence 
includes in it existence, in order to know thought 
and existence as its attributes, and individual beings as 
their modes. The arrangement and connection of 
thoughts correspond to the arrangement and connec- 
tion of things. The philosophical method is identical 
with the mathematical. 


[' Translated into English by Prof. Baynes, 2nd ed. 1851, Edin. ] 





a a ae a a a een — 





TE nenn ers 


awe 

















48 





Of the works of Spinoza, the Tractatus de Intellectus 
Emendatione, in the Opera Posthuma, Amstelod. 1677, belongs 
more especially to our subject. Several passages in the Ethics 
are to be compared with it. The fundamental postulate of 
Spinoza is: ‘ Ut mens nostra omnino referat naturae exem- 
plar, debet omnes suas ideas producere ab ea, quae refert 
originem et fontem totius naturae, ut ipsa etiam sit fons cete- 
rarum idearum.’ He defines truth to be ‘ convenientiam ideae 


cum suo ideato.’ He distinguishes three kinds or grades of 


knowledge: imaginatio (φαντασία), ratio (the ἐπιστήμη of 
Aristotle), and intellectus (the intuitive knowledge of prin- 
ciples, almost equivalent to the Aristotelian vods). The phi- 
losopher considers all things as moments of one substance, 
sub specie aeternitatis. The “ concatenatio intellectus ’ should 


ς concatenationem naturae referre.’ 
Kuffeler treats of the method of philosophical investigation 


from the stand-point of Spinoza, in his Specimen Artis Ratio- 
cinandi naturalis et artificialis, ad pantosophiae principia 


manducens, Hamb., 1684. 
§ 26. Locke (1632-1704), applying the method of 
Bacon to the objects of inner experience, investigated 


the psychological problem of the origin of human know- 


ledge, with the view of reaching a sure fundamental 
position for the decision of the logical question (of the 
question belonging to the theory of knowledge) of the 
objective truth of our notions. Locke distinguished 


sensation or sense-perception from reflection or percep- 
tion of the inner activities to which the soul is aroused 
on occasion of the outer affections. From these two 
sources all conceptions.arise. There are no ‘innate ideas.’ 
Nihil est intelleetu, quod non fuerit in sensu. Locke, 
like Des Cartes, attributes full truth to the internal per- 
ceptions, partial truth only to the external. Locke, by 


his results, was the forerunner of the sensationalism of 








+ 


$ 27. Leibniz and Wolf. 15 





Condillac, who- sought to reduce all reflection to sensa- 
tion, and by his method the forerunner of the Ideal- 
πὰς of Berkeley, of the S&epticism of Hume, of the 
Empiricism of the Scottish School, and of the Critical 
Philosophy of Kant. 


Locke’s chief work, An Essay concerning the Human 
Understanding, was first published in London, 1690 Since he 
would not admit that the conceptions arrived at ἫΝ sense-per- 
ception are true pietures of the objects (figure in space ma 
be objective; colours, sounds, &c. are not), he limited the 
truth of our thoughts to the objectively correct union and 
separation of the signs of things." Connected with Locke are 
J. P. de Crousaz,? Is. Watt? Condillac,‘ and Hume.’ The 
Idealism of Berkeley® (1685-1753), according to which onl 
spirits and their ideas exist, since all unthinkine objects = 
ideas of a percipient and thinking existence, and the Scottish 
chool ( Reid, Stewart, &c.), which returned to the rin of 
innate activities as facts of inner experience, are, in spite of 


their polemic against it, essentially connected with the Lockian 
tendency. | 


§ 27. Leibniz (1646-1716) maintained against Locke 
the doctrine of innate ideas; but he ee αὐτὴν 
part of the contents of consciousness to be the produc- 
tion of the inner self-development of the mind (Seele). 
Leibniz found warrant for the objective truth of clear 
and distinct conceptions in a harmony between the soul 


1 Essay, bk. iv. ch. v. ὃ 2. 
2 La Logique, Amst. 1712. 3 Logic, 1736 
4 " . 2 4 , . . Ἢ s 
Essai sur Ü’Origine des Connaissances humaines, 1745; T'raité des 
Sensations, 1754 ; Logique, 1781. 
5 . . 
Enquiry concerning the Human Understanding, 1748 Fbest_edition- 
by -‘T-H- Green-and “PAF 701- 


πα, ’ - 


a [Best edition is the Collected Works of George Berkeley, D.D. 
ishop of Cloyne, ed. by Prof. Fraser, Clarendon Press, 1871. | 


E 














— 


§ 27. Leibniz and Wolf. 


50 


— 


| BR ‘hed Ὁ God. Error arises 
and outer things pre established by Deck and 


from a want of clearness and distinctness. > 
confused knowledge may be raised by ge " 
clearness and distinctness. Leibniz (in oppos! ion ei 
Des Cartes) declared the logical rules to be “ , 
ο be despised, because correctness of demon 
d on their being followed. He held the 


principles of Contradiction and of Sufficient Reason to 


be the most general principles of all demonstration. 2 

Taking his stand upon the Leibnizian theory, Wol ἢ 

od Logie (as he did all the philosophical discı- 
= 


lines) ording to mathe- 
lines ΜΝ 

ce method. He treated Logic as the doctrine E 
knowledge, and placed the logical forms ın kan 
relation both to ontological forms and psychological laws. 
the doctrine of knowledge are 


in hi Üssals 
contained partly in small tracts, partly in his a. 
in. directed against Locke, ἃ 
sur l’Entendement humain, d agair ock ze 
published posthumously by Raspe, ın ag nie Ἂν μι 
᾿ Sli rincl uicqul | 
f the Cartesian principle, ἢ 
— i ipio, 1 ° de ea enun- 
j j : id est verum seu 
distincte de re aliqua perciplo, u. 
ciabile;’ but he held it necessary to prevent Ee πρὸς 
; » . BR ss 
abuse of the principle by laying down criteria of clearn | 
and distinctness. He, accordingly, defines the u =. 
tion (notio clara) to be that which can recognise the objec 
istinguish it from others. The clear concep- 
ς ἃ distinct (dis- 
the particular 


truth not to b 
stration depende 


pre | 
in systematic connection, ace 


The opinions of Leibniz upon 


conceived, and d ; 
tion is either confused (confusa) or definite an 


tincta). Confusion is want of clearness in 
attributes (notae). Distinetness or definiteness, 


hand, is the clearness of the particu 
which together make up the conception. 


conceptions there 1s no 


the attributes of the attributes, on to the | 





on the other 
lar individual attributes 
In absolutely simple 
distinction between clearness and dis- 


‚hen 
tinctness. The distinct conception, finally, 1s adequate Se 
he attrit ast simple elements, 





δ 27. Lebuiz and Wolf. 51 








are clearly conceived.! These definitions are not in them- 
selves free from fault. Distinctness and Confusion are spe- 
cifically, not gradually, to be distinguished from Clearness and 
Unclearness, just as the accuracy and inaccuracy of a drawing 
are from the clearer and fainter outline. But the system ot 
Pre-established Harmony cannot admit that error has a source 
specifically distinct from that of want of clearness. The possi- 
bility, which consists in freedom from inner contradiction, and 
becomes known by the complete resolution of conceptions into 
their component parts, is, according to Leibniz, the warrant of 
objective validity or truth. He says, in the above quoted tract: 

‘ Patet etiam, quae tandem sit idea vera, quae falsa ; vera scilicet 
quum notio est possibilis, falsa quum contradictionem involvit.’ 
By the separation of a conception into its non-contradictory at- 

tributes, we recognise ἃ priori its validity, but we recognise 
ἃ posteriori its validity by experience. The truth of a 
proposition consists in its correspondence with the objects to 

which it refers. It is reached by accurate experience and 

correct logical proof. Meditationes (as above): De caetero 

non contemnenda veritatis enunciationum criteria sunt regulae 

communis Logicae, quibus etiam Geometrae utuntur, ut 

scilicet nihil admittatur pro certo, nisi accurata experientia 

vel firma demonstratione probatum ; firma autem demonstratio 

est, quae praescriptam a Logica formam servat. For the 

principles of contradiction and sufficient reason as the grounds 

of all demonstration, see the Monadology (Principia Philoso- 
phiae), §§ 30-31. Leibniz wished to see a doctrine of pro- 
bability added to Logic, as a second part. 

Christian Wolff gave a systematic representation of Logic 
in his shorter German treatise— Vernünftige Gedanken von 
den Kriften des menschlichen Verstandes, 1710; and in his 
extensive work—Philosophia Rationalis sive Logica, 1728. 
He defined Logic to be scientiam dirigendi facultatem cogno- 
scitivam in cognoscenda veritate.2 The rules, according to 


1 See Leibnitii Meditationes de Cognitione, Veritate et Ideis | appended 
to Prof. Baynes’ ed. of the Port-Royal Logic, 2nd ed. pp. 424-30]. 
2 Log. Discursus Praeliminaris, § 61; Prolegomena, § 10. 


E 2 














| 27. Leibniz and Wolf. 


52 


— 


which the human mind learns the essences of things, must = 
the one hand be psychological, and on the other en 
principles." It is advisable, because of its ger we 
Didactic, that Logic should precede Ontology and Psychology 
and so Wolff makes it.’ The proof, however, of the “ee 
axioms is not, therefore, to be omitted, but the more import- 
ant doctrines of Ontology and Psychology must be agen 
posed in Logic, where they from the first vindicate μονὴ 
position, both by immediate evidence, and by their ee 
with experience. Accordingly, vo places some psye = 
logical considerations,* and a section ‘de = “ us 2 
generalibus entis,’® at the head of his logica systenl. 
divides Logic into theoretical and practical. The ἜΝ 
treats of Notion, Judgment, and Inference 5 the latter, 0 
the use of Logic in judging, and in the investigation a 
in the study and composition of books, in the ae ar 
knowledge, in the comparative valuing of the individua 


stly, 1 acti ife, and in 
powers of knowledge, and, lastly, in the practice of life, 


the study of Logic itself. Wolff gives as the nominal definition 
of -truth—‘ Est veritas consensus iudici nostri ange! ana 
seu re repraesentata τ᾿" and as its real definition—* Verttse 
est determinabilitas praedicati per notionem subiectl. T #6 
possible notion corresponds to the true affirmative judgment. 
Possibility consists in absence of contradiction.” To this 
(Leibnizian) criterion Wolff refers the Cartesian, and also the 
a by Z'schirnhausen (1651-1708), 


criterion of conceivability given Dy - oh | 
the contemporary of Leibniz, in his Medicina Mentis, 1687— 


‘yerum est quiequid concipi potest, falsum vero quod non 


. .« 210 
coneipi potest. Σ ας Ξ : 
‘ ὡς S SC "n> 
Among the contemporaries of Leibniz, besides Tschir 


hausen, Christian Thomasius (1655-1728) 1s to be mentioned, 


- ; ’ 5 9 > 
1 Discursus Prael. § 89; Prolegom. § 28. | 
2 Discurs. Praclim. § 91: ‘Methodum studendi praeferre maluimus 


methodo demonstrandi.’ 
3 Log. §§ 2, 28. 
6 Ibid. ὃ 505. 
9 Ibid. § 518. 


4 Ibid. ὃ 30 ff. 
7 Ibid. $ 513. 


5 Ibid. § 59 ff. 
8 Ibid. § 520. 











§ 27. Leibniz and Wolff. 53 





who sought to make Logic more practical, and believed that 
he had pointed out a middle way between the Aristotelian 
and Cartesian Logics. His special service (as Wolff’s was 
later) consisted in teaching men by his example to express 
scientific thought in the German language. Among the 
opponents of Wolff are to be mentioned Lange, Crustus, 
Daries, and Euler. More or less nearly related to Wolff are 
Baumeister, Baumgarten, Meier, Reimarus,' and Ploucquet.” 
Lambert, with much which lacks substance and logical form, 
gives much that has meaning and originality. His Neues 
Organon ® is divided into four parts, which Lambert calls— 
Dianoiologie, Alethiologie, Semiotik, and Phänomenologie. 
According to his explanation, they comprehend more com- 
pletely what Aristotle and, after him, Bacon have called an 
organon. These sciences are ‘instrumental,’ or are instru- 
ments of the human understanding in the examination of 
truth. Dianoiologie is, according to Lambert, the doctrine of 
the laws of thought which the understanding must follow if it 
would advance from truth to truth. Alethiologie is the 
doctrine of truth, in so far as it is opposed to error, of the 
possibility of knowing truth. Semiotik is the doctrine of the 
expression of thought (especially of its expression in language). 
Phänomenologie is the doctrine of error, and of the means 
of avoiding it. Bilfinger (who wished also a logical theory 
for the ‘subordinate cognitive faculties’), Feder,‘ Eberhard, 
and Ernst Platner® proceeded more or less on Leibnizian 
principles. 


I Vernunftlehre, 1756; 5th ed. 1790. 

2 Methodus calculandi in Logicis, 1753 ; Methodus tam demonstrandi 
Omnes Syllogismorum Species, quam Vitia Formae detegendi ope unius 
Reyulae, 1763. 

3 Leipzig, 1764. 

4 Grundsätze der Logik und Metaphysik, 1769, and Institutiones 
Logicae et Metaphysicae, 1777. 

5 Allgemeine Theorie des Denkens und des Empfindens, 1776. 

6 Philo. Aphorismen, 1776, and Lehrbuch der Log. und Metaph. 


1795. 








54 § 28. Kant. 


Mannes 


$ 28. Kant (1724-1804) denied the identity of elear- 
ness, distinctness, and absence of contradiction, with the 
material truth of knowledge, which had been asserted 
by Des Cartes and Leibniz. He returned to Locke’s 
view, that the origin of knowledge can alone decide 
upon its truth, without adopting Locke’s theory of the 
empirical origin of all human knowledge. Accordingly, 
Kant investigated anew, 'n his Kritik der reinen Ver- 
nunft, the origin, extent, and limits of human knowledge. 
He distinguished analytical or explanatory judgments, 
which alone rest upen the axiom of contradiction, from 
synthetic or amplifying judgments, and, among the latter, 
judgments which have an accidental limited validity 
from those by which the universal and the necessary 1s 
known. Kant believed that all strict generality and 
necessity must be traced back to an origin & priori, 1.6. 
a purely subjective origin independent of all experience. 
His presupposition ruled his whole course of thought, 
and involved a leap from apodicticity to the merely 
subjective, accomplished by means of the ambiguous 
middle term ἃ priori. Under its influence he proceeded 
from the fundamental question, ‘How are synthetic judg- 
ments & priori possible?” to the result, that the material 
of knowledge comes to us from without by means of 
the sense-affections, but that ‘ts forms are added ἃ priori 
by the human mind. These ἃ priori forms of knowledge 
are, according to Kant: (a) the forms of Intuition of 
outer and inner sense ;—(b) the T welve Categories, or the 
pure original notions of the understanding: (1) Three 
Categories of Quantity— Unity, Plurality, Totality ; (2) 
‘Three Categories of Quality—Reality, Negation, Limita- 


§ 28. Kant. 55 





ip (3) Three Categories of Relation—Substantiality 
Causality, Reciprocity ; (4) Three Categories of Modality 
—Possibility, Existence, Necessity ;—(c) the ideas of 
reason—of the Soul, the World, and God. These a 
priori elements of knowledge, because of their subjec- 
tive origin, are, according to Kant, unable to reveal to 
us the peculiar essence of things. Human knowledge 
extends only to the world of phenomena, into which val 
unconsciously bring these forms, and which must shape 
itself according to them. It cannot extend to things 
as they exist in themselves, or as they exist μον 
our capacities of knowledge. Consequently, no theoreti- 
cal insight into the essence of the human soul, of the 
intelligible world, and of God, can be reached. We can 
however attain a securer practical faith from the ground 
of the moral conscience. All these considerations, be- 
longing to the theory of knowledge, Kant separates com- 
pletely from general formal Logic. He defines this to 
be the rational science of the necessary laws of thought 
as they have to do with, not their particular objects taal 
all objects generally ;—or the science of the pure Sine of 
thought in general ;—or the science of the right use of 
the understanding and reason, according to a priori 
principles, as the understanding thinks. Kant divides 
general Logic into pure and applied. The former 
treats of the understanding considered in itself; the 
latter, which belongs to psychology, treats of the under- 
standing in its conjunction with the other psycho- 
logical faculties. Pure general Logic is divided into 
the doctrine of the elements and the doctrine of method. 
Special Logic treats of the special methods of the par- 








56 § 28, Kant. 





ticular sciences. Transcendental Logic belongs to the 
Kritik of Pure Reason, and forms that part of it which 
treats of the categories of the understanding and their 
worth in knowledge. Pure general Logic endeavours 
to comprehend thoroughly the forms of thought, ab- 
stracting them from every metaphysical and psycholo- 
gical-relation, and only allowing reference to the laws 
of Identity and Contradiction. This tendency produces 
the subjectively formal character of the Kantian Logic. 


Kant’s chief theoretical work, the Kritik der reinen Ver- 
nunft, first appeared in 1781, was formally remodelled in the 
second edition! of 1787, and since then has appeared unchanged 


1 Kant expressly says, in his preface to the second edition, that the 
remodelling. has to do with the form of representation only, not with 
the contents. For the realist moment, which is not wanting in the first 
edition, but is kept in the background because self-evident, is expressed 
more distinctly and forcibly in the second edition, in order to oppose ἃ 
misunderstanding introduced in a review, which has overlooked it, and 
made Kant’s doctrine approach to near to that of Berkeley. Yet Michelet 
Schopenhauer and others have believed that they can see a reconstruc- 
tion of the Kantian stand-point itself. But Ihave endeavoured to show in 
my tractate (De priore et posteriore Forma Kantianae Critices Rationis 
Purae, Berol. 1862) that Kant's assertion is confirmed by a thorough 
comparison of the two editions, and retain my opinion after Michelet’s 
answer,* who, with his Hegelian tendencies, makes the ‘ things-in-them- 
selves,’ which give the matter to the empirical intuitions, mean ἡ the 
unity of Essence in the manifold of phenomena.’ Michelet and 
Schwegler assert that Kant in the first edition of his Kritik of Pure 
Reason expresses the opinion that the Ego and the thing-in-itself may 
be one and the same thinking substance, and that he may therefore 
here enunciate hypothetically what Fichte afterwards taught, that the 
Ego is not affected by a strange thing-in-itself, but purely by itself. 
But these assertions of Michelet and Schwegler rest on a misinterpreta- 
tion of the passages quoted.f Kant does not believe that the Ego 


* Gedanke, iii. pp. 227-48, 1562. 
t Krit. ἃ. r, Vern. Ist ed. 357-359, 379 f. 


§ 28. Kant. 57 


—- 





in the later editions. The Logic was published by Jäsche in 
1800, with Kant’s manuscript notes and scelanaitinn on his 
copy af Meyer’s Handbook of Logic (which Kant purposel 
added to his Lectures). In Logic Kant was connected with 
Reimarus in several ways, partly agreeing with him, partly 
combating him. Kant seeks to establish his isolation of 
Formal Logic by the axiom that sciences are not increased 
but disfigured, when their boundaries are allowed to run . 
each other. The limits of Logic, he says, are enough defined b 
this, that it is a science which fully represents and peed 
proves nothing save the formal laws of all thinking. Locks 
since Aristotle’s time, has followed the sure course of a a 
It has taken no step backwards, i.e. it has not needed to av 
up any of Aristotle’s acquisitions as useless and illusory ; wit 
it has made no advance, and has not been able to ER an 
essential development. It must thank its narrowness onl fox 
its scientific certainty and completeness, which mtl ak 
compels it to withdraw its attention from every object of 
knowledge and from the differences of objects, and limit its 
enquiries to the understanding only in itself and in its forms.! 
Of course we must recognise with Kant that the liens οἷ 
Logic is the correct form of thought. We must also allow 
that Logic cannot have the same problem as Metaphysics and 
Psychology, and that it does not teach single parts of diese 
sciences. But it is by no means to be granted that Logic as a 
science does not need to refer to psychological and metaphysical 
principles, in order to establish its laws concerning the correct 
form of thought. Therapeutic, as the science re restora- 
tion of health, or of the correct form of corporeal life, does not 


teach physiology or general natural science either wholly or 


affects itself merely, but holds that a substance different from us 
which, if it affects us, is perceived by us to be in space, can itself 
appear to be a thinking essence.* 

I Kritik d. reinen Vernunft, 2nd ed. pref. viii. ix.; cf. p. 74 f£.; ard 
Logik, p. 3 ff. Werke, Hart. ed. viii. 12 ff. de ἘΞ 








* Cf. my remarks in my Grundr. der I u 3 
ond ed., Berlin, 1868, pp. a ee! r Gesch. der Phil. iii. § 16, 











58 § 28. Kant. 








in part, but it must refer to the principles of these two 
sciences in order to give its prescriptions a scientific basis. 
That form of thought is the correct one which capacitates the 
human spirit for the knowledge of things, and therefore the 
double reference is indispensable in Logic (cf. § 2). The 
abstraction of the relations of the forms of thought to the 
forms of existence, to the psychological laws, and to the con- 
tents of thought in general (which is to be carefully distin- 
guished from the several contents of thinking), and their 
separation from the forms of perception—in short, the removal 
of the harder problems—has undoubtedly its advantages in 
didactic reference. Such a representation of Logic may be 
suitable as a preliminary propaedeutic, and perhaps now and 
then indispensable ; but if it be taken, and if it be reckoned, 
as the last and highest representation, it robs Logic of an 
essential part of its scientific character. If the fundamental 
doctrine of Kant were true, that the things-in-themselves 
are unknowable, then the logical forms, to be scientifically 
understood, must be taken with reference to the metaphysical 
forms of the world of phenomena (Substantiality, Causality, 
&c.). Kant himself recognises this in his Kritik der reinen 
Vernunft, at least in reference to the judgment, where he 
(p. 140, 2nd ed.) blames as insufficient its explanation as the 
conception of a relation between two notions, and prefers the 
definition —it is an objectively valid relation (p. 142)—it is the 
way to bring given knowledge to the objective unity of apper- 
ception (p. 141); and where, in accordance with this, he refers 
the functions of the judgment to the categories, because the 
metaphysical categories express the different objective relations. 
For example, the logical relation of subject and predicate, in 
the categorical judgment, is related, according to Kant, to the 
metaphysical relation of Subsistence and Inherence, the logical 
relation of the conditioning and conditioned judgment to the 
metaphysical relation of Causality and Dependence, and so on. 
Had Kant kept to this stand-point in his Logic, and consistently 
followed it out, the science would have got from him, in all 
essential points, the place afterwards given it by Lotze. But 


§ 29. Kantian School, etc. Fries. Herbart. 59 





Kant has not let that knowledge bring forth fruit for his Logic. 
He abstracts the science from all objective relations. When it 
is seen that Kant’s fundamental doctrine, that real objects are 
unknowable, is untenable, and that metaphysical forms have a 
real meaning, as will be shown in our systematic development 
of Logic, this abstraction will be found to be still less scien- 
tifically justifiable. The limits of knowledge set up by Kant 
are not, however, to be violently broken through, either by an 
axiom postulating the identity of thought and existence, or by 
an unconscious transference of the laws of thought to things 
in themselves. They are to be gradually, as it were, and 
methodically levelled and removed, and to accomplish this task 
is the aim of this work." 

Kant’s fallacy may be put shortly,— What is apodictic is 
ä priori; what is ἃ priori is merely subjective (without relation 
to ‘ things-in-themselves’); therefore, what is apodictic is 
merely subjective (without relation to ‘ things-in-themselves’). 
The first premise (the minor), however, is wrong if ἃ priori is 
understood in the Kantian sense to mean being independent of 
all experience. Kant wrongly believes that certainty to be a 
priori (independent of all experience) which we really attain 
by a combination of many experiences with one another 
according to logical laws; and these laws are conditioned by 
the reference of the subject to the objective reality, and are not 
ἃ priori forms. He erroneously maintains that all orderly 
arrangement (both that in time and space and that which is 
causal) is merely subjective. 

Upon the relation of the Kantian Logic to the Aristotelian, 


ef. §§ 2, 16. 


§ 29. The Logic of Kant’s School—viz. of Jacob, Kıese- 


wetter, Hofbauer, Maass, Krug, &c.—is to be treated in 


the same way as Kant’s. The logical works of A. D. Chr. 


1 Cf. specially §§ 38, 40-44, and the remarks to δὲ 129, 131, 137; 
ef. also my tractate upon Idealismus, Realismus und Idealrealismus in 
Fichte’s Zeitschr. für Philos. xxxiv. 63-80, 1859. 








60 ὃ 29. Kantian School, etc. Fries. Herbart. 





Twesten, Ernst Reinhold, Bachmann, Friedrich Fischer, 
&e. are more or less related to this formal stand-point. 
Fries gives Logic a psychological foundation. He under- 
stands Logic to be the science of the laws of thought, and 
divides it into: Pure Logic, which treats of the forms 
of thought; and Applied Logic, which treats of the 
relation of these forms of thought to the whole of human 
science. Pure Logic, again, is divided into Anthropo- 
logical Logic, which considers thought as an activity of 
the human spirit; and Philosophical or Demonstrative 
Logic, which enunciates the laws of the thinkable. He 
divides Applied Logic into the doctrine of the relation 
of thought to knowledge in general, the doctrine of the 
laws of knowledge which has been thought, or of the 
illumination of our knowledge, and the doctrine of 
method. Friedrich van Calker is allied to Fries. He 
explains the doctrine of thought, or Logic and Dialectic, 
to be the science of the form of the higher consciousness ; 
and divides it into the doctrines of experience, laws, 
and art of thinking. 

Herbart defines Logic to be the science which treats 
generally of distinctness in notions and the connection 
(arising out of this) of these notions to judgments and 


inferences. He entirely separates from Logic, and refers 
to Metaphysics, the question of the significance of the 
forms of thought in knowledge. He believes that the 
logical laws neither can nor should be established on a 
scientific basis by means of metaphysical and psycho- 


logical considerations. 
‘ Allied to Herbart are Drobisch, Hartenstein, Waitz, 
Allihn, and others. 





§ 30. Fichte, Schelling, and their School. 6L 





The logical works which proceed from the Kantian School, 
or which essentially share its tendency, refrain from entering 
upon the deeper problems, and do not make up for this 
want by perfect accuracy, sufficiency, and clearness in the 
problems to which they have limited themselves. Jacob’s 
Grundriss der allgemeinen Logik appeared first in 1788; 
Kiesewetter’s Grundriss der Logik in 1791; Hoffbauer’s 
Analytik der Urtheile und Schliisse in 1792, and his An- 
fangsgründe der Logik in 1794 ; Maass’s Grundriss der Logik 
in 1793; Krug’s Logik oder Denklehre in 1806; Ernst 
Reinhold’s Versuch einer Begründung und neuen Darstellung 
der logischen Formen in 1819; Logik oder allgemeine Denk- 
formenlehre in 1827; Theorie des menschlichen Erkennt- 
nissvermögens in 1832; Twesten’s Logik, especially the 
Analytic, 1825; Bachmann’s System der Logik in 1828 
(a very instructive work); Friedr. Fischer’s Lehrbuch der 
Logik in 1838; Fries’ Grundriss und System der Logik, 1811; 
Herbart’s Lehrbuch zur Einleitung in die Philosophie, 1813 
(5th ed. 1850), in which §§ 33-71 contain an epitome of Logic ; 
Drobisch, Neue Darstellung der Logik nach ihren einfachsten 
Verhältnissen, nebst einem logisch-mathematischen Anhange, 
1836 (2nd completely remodelled edition, 1851; 3rd edition 
written afresh, 1863; worth looking at as the best repre- 
sentation of Logic from that stand-point, very valuable for its 
clearness, acuteness, and relative completeness). 


§ 30. Fichte (1762-1814), in his Wissenschaftsiehre, 
in order to overcome the inner contradiction of the 
Kantian doctrine of knowledge, traced not only the 
form, but also the material of knowledge to the thinking- 
subject, or the Ego exclusively, and thereby established 
a subjective idealism in the strictest sense. He con- 
sidered Formal Logic no philosophical science, because 
it broke up the connection in which the form and content 
of knowledge stand to each other and to the highest 
principles of knowledge. 





62 § 30. Fichte, Schelling, and their School. 





Schelling (1775-1854) passed a like judgment upon 


Formal Logic. He also traced form and content, and 
therefore the subjective and objective reason, back to one 
single prineiple—the Absolute, whose existence he be- 
lieved to be known by an intellectual intuition. 

Neither has developed Logic itself. 


Johann Gottlieb Fichte, in his work upon the Begriff der 
Wissenschaftslehre (1794), laid down the postulate, that all 
science should be derived from one simple principle, and 
sought in his Grundlage der gesammten Wissenschaftslehre 
to satisfy this postulate by deducing all knowledge, both in 
content and form, from the principle of the Ego. He con- 
siders the logical axioms to be the cognitive basis of the 
higher axioms of the Wissenschaftslehre, and these again the 
real basis of the former. Fichte at first wished to make 
Formal Logic co-ordinate with the Transcendental, as Kant 
had done, but later! he sought to abolish it altogether, and 
supplant it by the Transcendental Logic. He accuses it of 
assuming as granted that which is itself the product of the 
thought to be explained, and therefore of reasoning in a circle 
when it attempts to explain thinking. 

Schelling teaches that the original content and the original 
form of science are conditioned the one by the other. The 
principle of all science is the point whence by an indivisible 
act of intelligence the form and content of science spring up 
together. If Logic arises in a scientific way, its fundamental 
principles must proceed by abstraction from the highest 
axioms of knowledge. Logic, in its usual pure formal state, 
belongs wholly to empirical attempts in philosophy. Dialectic 
is, according to Schelling, Logic, in so far as it is the science 
of the form and the pure’art of Philosophy.’ 


1 Particularly in his lecture on the relation of Logic to Philosopliy 
in his Posthumous Works, ed. by 1. H. Fichte (Bonn, 1834-35), i. 111 f. 

2 System des transcendentalen Idealismus, pp. 35-37, 1800; Lectures 
on the Methode des Akademischen Studiums, pp. 17 f£., 122-29, 1808. 


I 


§ 31. Hegel. 63 








Franz von Baader’s view (1765-1841) is also related to 
Schelling’s. The School of Baader distinguish theosophic 
from anthroposophic Logic, which are related as original and 
copy. The former considers the totality of the absolute 
forms of thought and knowledge of the infinite spirit; the latter, 
the totality of the laws and forms which the copying know- 
ledge of the finite spirit obeys. Franz Hoffman,' conformably 
to Baader’s principles, represents the divine knowledge a 
moment of the divine immanent process of life. Krause’s Logic 
and Schleiermacher’s Dialectic (cf. § 33) are also essentially 
related to Schelling’s principles. 


§ 31. Hegel (1770-1831), following the principles of 
Fichte and Schelling, founded the Metaphysical Logic. 
Kant held that the form and content of thought were 
mutually independent, and referred the form exclusively 
to the thinking spirit, and the content exclusively to 
the things affecting. Hegel’s Logic, on the contrary, 
rests on the double identification of: (1) Form and 
Content; (2) Thought and Being. Hegel judged (1), 
with Fichte and Schelling, that a separation of form and 
content is inadmissible, and that the most general con- 
tent of knowledge must be conceived along with the 
form. (2) With Schelling, he believed that the necessary 
thoughts of the human spirit, according to content and 
form, stand in absolute correspondence to the essence 
and forms of the development of things. Hegel adds 
(3) the postulate of method, that pure thought in its 
dialectical self-development advances creatively from 

I In the work Speculative Entwicklung der ewigen Selbsterzeugung 
Gottes, Amberg, 1835, and in the Vorhalle zur speculativen Lehre Franz 
Baader’s, Aschaffenburg, 1836. Cf. also Hoffmann, Grundzüge einer 


Geschichte des Begriffs der Logik in Deutschland von Kant bis Baader, 
Leip. 1851. 





64 


the widest and most abstract notions to the ever fuller 
and more concrete up to the absolutely highest, by means 
of negation and identity dwelling in the notions, and 
also in absolute unity with the self-production of 
existence, so that the subjective necessity of thought 
must be also the criterion of objective truth. Hegel’s 
Logic traces this self-development of the notion from 
pure being up to the absolute idea; his natural philosophy 
from space and time up to the animal organism; and 
his philosophy of the spirit from the subjective up to 
the absolute divine spirit. Logic is, according to Hegel, 
the system of pure reason, —thought as it is in itself 
without its wrappings,—the science of the pure idea, 
i.e. of the idea in its being in-and-for-itself,—or the idea 
in the abstract element of its being. It divides into 
three parts: the doctrine of being, of essence, and of 
the notion. The first part treats of the categories of 
Quantity, Quality, and Proportion ; the second, of the 
essence as the ground of Existence, of the Phenomenon, 
and of the Actual; the third, of the Subjective Notion 
(i.e. of the Notion, Judgment, and Inference), of Ob- 
jectivity (ie. of Mechanism, Chemism, T eleology), and 
of the Idea. The moments of the idea are life, know- 
ledge, and the abstract idea. The abstract idea is the 
abstract truth,—the idea thinking itself,—the pure 
form of the notion which perceives its content to be 
itself. In the doctrine’ of the Subjective Notion Hegel 
brings in the chief definitions of Formal Logic, but he 
submits them to an essential transformation, according 
to the demands of the Dialectic method, and at the same 








time gives them an objective significance. 


§ 31. Hegel. 5 





Hegel's logical works are— Wissenschaft der Logik, 1812-16, 
2nd ed. 1833-34 (I. Objective Logic: A. The doctrine of Being ; 
B. The doctrine of Essence.—II. Subjective Logic), and En- 
cyclopädie der philosophischen Wissenschaften im Grundrisse, 
1817; the first part, the Science of Logic, §§ 19-244. The 
more Hegel’s polemic is justifiable the less are his own defini- 
nitions tenable. He justly blames Kant’s attempt to abstract 
Logic from all relation to existence; but he himself has gone to 
the opposite extreme of exaggerated identification. ‘ The critical 
method separates what God has joined, the method of identifi- 
cation would unite what God has separated ’ (Troxler). 

1. As to the identification of the sciences of the form and 
of the most general content of Thought, ie. of Logic and 
Metaphysics. It is true that form and content are not inde- 
pendent of each other and demand a scientific explanation of 
their opposite relations, but nevertheless they make two essen- 
tially different objects of knowledge, whose consideration ac- 
cordingly engages two distinct branches of the one whole 
philosophical science. A separate representation of Logic, if the 
metaphysical relations are not disowned, is not only admissible, 
but also a necessary condition of scientific completeness. Schel- 
ling, among others, recognises it to be legitimate when he be- 
lieves Dialectic, the science of the form of philosophical thought, 
to be a science philosophically correct, and considers admissible, 
as a special power in the universal science of reason, a Logic 
which derives the laws of ‘reflexive knowledge’ from speculative 
grounds. The union of the sciences by Plato (which, besides, 
was only relative) was natural in that stage of origination, 
when both sciences began to develope themselves from the 
common germ of philosophical thinking. The complete isola- 
tion of Logic from metaphysics, on the other hand, was an 
error, which had for its basis the right feeling that a strict 
distinction of the two sciences was necessary. A return for a 
time to the old state of union might be good as a reaction 
against this isolation with its empty, barren abstractions; but, 
in the long run, it is difficult to deny that the true connection 
lies in relative independence. Hence those categories of which 


F 





66 § 31. Hegel. 





Hegel treats in the two chief divisions, of Being and of 
Essence, should be taken out of Logic and relegated to 
Metaphysics. Further, what Hegel introduced in the section 
on Objectivity (Mechanism, Chemism, and Teleology) belongs 
to natural philosophy. Only the problems which Hegel treats 
of in the section upon the Subjective Notion, and partly those 
in the section on the Idea, belong to Logic. The proper place 
of Logic, which is the doctrine of knowledge, is not within 





Metaphysics (although it may precede it as a propaedeutic, = 
$ 7), but among the subordinate sciences of the philosophy o 
ir] . § 6. 
ER a identity of the forms of thought with the 
forms of existence, and especially the objective meaning as- 
signed to the Notion, J udgment, and Inference. reas has 
thought that he has here also discovered a relation of sameness, 
while there is really only that of reciprocal reference and of 
parallelism. Notion, judgment, and inference are forms of the 
thinking and knowing spirit. They find their correlates in the 
objects of knowledge—the notion in the essence of things, the 
judgment in the relation of subsistence and inherence, inference 
in the regular connectedness of what actually happens. In 
opposition to the Subjectively-formal Logic, which disowns 
these relations, one might be reminded of them in the para- 
doxical form—‘ The notion is immanent in things, things 
judge and infer, the planetary system, the state, everything in 
accordance with reason, is an inference.’ Expressions of this 
kind are true as poetical metaphors, and very appropriate to 
awaken deeper reflection; but they cannot be considered to 
be strictly scientific, for they include under the same notion 
forms of thought and existence which are related only - 
certain essential determinations, but do not agree in all. 
Hegel has hardly touched upon the problem of how far the 


1 This figurative character is recognised by Zeller in his introductory 
lecture at Heidelberg, Ueber die Bedeutung und Aufgabe der Er- 
kenntniss- Theorie, p. 6, Heidelb. 1862. Michelet endeavours to justify 
the Hegelian stand-point, in opposition to this, in his journal, Der 


Gedanke, iii. pt. 4, p. 288 ff., 1862. 





67 





forms of perception are related to the outer reality; yet if, 
whenever we speculate upon the manner and possibility of the 
affection, it is hardly to be denied that perception is brought 
about by a co-operation of the perceiving individual with the 
outer world, then Kant’s deliberate separation of a subjective 
and objective element in perception cannot be wholly rejected. 
The admission of a thorough-going agreement of the element 
added byjsubject with the peculiar existence of the outer world 
is at most only an uncertain hypothesis, and cannot once be 
maintained with reference to colours, sounds, &c. even as a 
mere hypothesis, in opposition to the results of modern physics 
and physiology. Cf. § 38. 
When Hegel generally rejects the whole Kantian attempt to 
test our capabilities for knowledge, because the knowledge of 
what knows cannot precede the knowledge of reality, we reply 
that the knowledge of what knows, although the second stage 
of knowledge in general, may quite well be the first stage in 
philosophical knowledge. Man’s activity of knowledge is first 
directed to the outward world, and gradually to many psycho- 
logical relations; then turned to critical reflection on itself 
and its own capacities for knowing ; and lastly, if the result of 
this testing process be a positive one, directs itself to reality in 
general, in nature and spirit. We must set out from faith, not 
from mistrust, in our own power of knowledge, if we are to 
reach any good result; but this faith, originally blind, must 
not remain a blind one. In so far as distinct grounds present 
themselves for denying material truth or agreement with ex- 
istence to perception or to thought in particulars or in ge- 
neral, these may not be set aside for the sake of this faith. 
This testing can only be carried out by thinking. We must 
trust to the power of the thinking which tests, to ascertain the 
right relations so long as definite reasons do not present them- 
selves for denying this power: the same holds good in again 
testing these grounds. This procedure does not lose itself in an 
ad infinitum, because no necessity compels the constant 
recurrence of new grounds for mistrusting the thinking which 
tests. At any one point a conclusion can be rightly attained, 


F 2 





68 ὁ 31. Hegel. 








as satisfactory as that in mathematical demonstration. Hegel’s 
axiom of an identity of thought and existence 1s — an 
escape from the Kantian criticism than a victory over it. 

3, The dialectic method sets before itself a false problem, 
and solves it only apparently. The problem is wrongly stated. 
For, just as from the Hegelian stand-point a morality is rightly 
demanded that may be above the compulsion of nature and yet 
not unnatural, so, in the province of the intellectual, the ana- 
logous proposition holds good, that thought should be free from 
the compulsion of experience but not void of experience. It 18 
not thinking, resting and remaining in itself, but thinking 
which works up the material originally obtained in outer and 
inner sense-perception according to laws founded on the idea 
of truth, that actually produces human knowledge and forms 
the object of consideration in Logic. The dialectic problem 1s 
insoluble. For: a. The more abstract notion cannot produce 
from itself alone the more concrete notion in the mind of 
the thinking subject, for ‘the product cannot contain more 
than what the factors have given’ (Beneke); and then Hegel 8 
single dialectic transitions really contain logical fallacies, as 
has been abundantly proved by acute opponents.’ b. When 


the dialectic process is transferred to reality, the ‘logical cate- - 


gories ’ are hypostatised and treated as independent essences, 
which are capable of a peculiar development and of passing 
over the one into the other. This is analogous to the Platonic 
hypostasis of ideas combated by Aristotle. How the outgoing 
in the objective reality from Being to Nothing, and then to 
Becoming, and so on to the Absolute Idea, can find place as ἃ 
timeless prius in the development of nature and spirit (treated 
of in the philosophy of nature and spirit), 1s neither con- 
ceivable nor thinkable; and it would contradict Hegel's prin- 
ciples to hold that the priority of the logical categories and 
their dialectical succession is a merely subjective abstraction. 


1 Cf the Author’s tract, Ueber Idealismus, Realismus und Idealreal- 
ismus, in Fichte’s Z. f. Philos. xxxiv. pp. 63-80, 1859. ; 

2 Especially by I. H. Fichte, Schelling, Trendelenburg, Kym, Lotze, 
Chalybiius, George, Ulrici, v. Hartmann, and the Herbartian School. 











§ 32. The Hegelian School $ 33. Schleiermacher. 69 





The truth which lies at the basis of the dialectical method is 
the teleological consideration of nature and mind (Geist), 
according to which both, advancing by means of the strife and 
change of opposites, are developed from the lower to the higher 
stages, by a necessity conformable to reason dwelling con- 
sciously or unconsciously in them. Human thought can know 
the gradual series of the developments, because this series rests 
on outer and inner experience. The dialectic method proceeds 
from notion to notion apparently by the purely logical mean 
of negative and identity, but really by this, that the thinker, 
whose consciousness is developed by other means, already per- 
ceives or anticipates each higher stage, and finds the lower, 
when compared with it, unsatisfactory. 


§ 32. Erdmann, Rosenkranz, Kuno Fischer, and others 
belonging to the Hegelian School, have partly repre- 
sented the system of Logic scientifically, partly treated 
the principle, method, and single problems of Logic in 
works of explanation or defence. 


The chief works of the Hegelian school are—J. E. Erdmann, 
Grundriss der Logik und Metaphysik, Halle, 1841, 4th ed. 
1864; Rosenkranz, Die Modificationen der Logik abgeleitet 
aus dem Begriffe des Denkens, Leipzig, 1846; System der 
Wissenschaft, ein philosophisches Enchiridion, Königsberg, 
1850; Wissenschaft der logischen Idee, Part I.: Metaphysik, 
Königsberg, 1858; Part II.: Logik und Ideenlehre, Königs- 
berg, 1859; Kuno Fischer, Logik und Metaphysik oder Wis- 
senschaftslehre, Heidelberg, 1852 ; 2nd ed. (wholly remodelled), 
1865. 


§ 33. Schleiermacher (1768-1834) means by Dia- 
lectic the art of scientific thinking, or the system of 
axioms for technical expression in the department 
of pure thinking. Pure thinking (in distinction 
from the artistic and from that of ordinary life) is 














70 § 33. Schleiermacher. 








thinking with a view to science. Science is what is 
identical in all the thinking minds producing it, and 
agrees with the existence which is thought about. 
The transcendental part of Dialectic considers the 
essence of science or the idea of science in itself; the 
formal or technical part considers the becoming of 
science or the idea of science in motion. Schleier- 
macher attacks the (Hegelian) position, that pure 
thought can have a peculiar beginning distinct from all 
other thinking, and arise originally as something 
specially for itself. He teaches that in every kind of 
thinking the activity of the reason can be exercised 
only on the basis of outer and inner perception, or that 
there can be no act without the ‘intellectual’ and none 
without the ‘ organic function,’ and that only a relative 
preponderance of the one or other function exists in 
the different ways of thinking. Agreement with exist- 
ence is immediately given in inner perception, and is 
attainable mediately also on the basis of outer percep- 
tion. The forms of thought, notion and judgment, are 
made parallel, by Schleiermacher, to analogous forms 
of real existence—the notion to the substantial forms, 
and the judgment to actions. 


Schleiermacher’s ‘ Dialektik ’ has been published by Jonas, 
in 1839, from his manuscripts and written lectures, as the 
second subdivision of the second volume of his literary 
remains, or as the second part of the fourth volume of the 
third division of his collected works. Schleiermacher has taken 
the idea and the name of Dialectic partly from Plato, partly 
from Schelling. He seeks to realise by actual representa- 
tion Schelling’s postulate of Dialectic as ‘a science of the 
form and as it were the pure art of philosophy.’ Schleier- 





δ 33. Schleiermacher. 71 





macher held that the technical form of scientific thought is 
separable by abstraction from its content, and forms the object 
of a relatively independent philosophical discipline. He 
recognised a parallelism but not an identity between the 
forms of thinking and knowing, and the forms of real exist- 
ence. He believes that thinking rests upon perception, and \ 

perception arises from the influence, affection, or impression / 

which comes from the objects or being without us. His views, Ὁ 
in all these relations, agree with the results of unprejudiced 
scientific investigation, and correspond more truly than Hegel’s 
do to the idea of the universe as one whole organism, in which 
the unity of the whole does not interfere with the manifold and 
relative independence of single sides and members; sameness 
in common fundamental characters does not remove or render 
meaningless difference in specific and individual properties, and 
no one member can be freed, with respect to his actions, or 
even his existence, from being conditioned by any other. On 
the other hand, we cannot agree with Schleiermacher when he 
puts the art of thinking in the place of Metaphysics, for the 
system of philosophy has room for both sciences, and assigns 
to each a special meaning and problem ($ 6). Again, Schleier- 
macher’s mode of defining the relation of thinking to per- 
ception, and the parallelism of forms of thought and forms of 
knowledge, appears to require correction in some particulars. 
This will afterwards be shown in our systematic representa- 
tion of Logic. Finally, we cannot approve of Schleiermacher’s 
division of Dialectic, according to which he distinguishes a 
transcendental from a technical or formal part; and, in the 
former, considers the notion and judgment, in their relation 
to the corresponding forms of existence, to be forms of science 
in itself; while in the latter, the syllogism, induction, deduc- 
tion, and the complex forms of thought, are considered to 
be forms of the genesis of science, or of the idea of science 
in motion. For the forms which Schleiermacher relegates to 
the second class, correspond to certain forms of existence, with 
this distinction only—that the notion and the judgment, 
the most elementary forms of thought, mirror the simplest 








72 § 34. The Latest German Loguczans. 





forms, while inference and the other ways of constiuction 
and combination mirror the wider and more general inter- 
dependence of existence. Schleiermacher is wrong when he 
says that these latter forms belong to the genesis of science, 
and become unmeaning and superfluous after MM thought 
has reached its completion in science; for complete science 
can only exist in them. Again, these forms have a relation 
to existence as ‘transcendental,’ and belong to ‘science as 
such’ as essentially as do the notion’ and judgment. They 
must therefore all be relegated to the ‘ transcendental part.’ 
There remains for the ‘ formal or technical part’ only certain 
psychological considerations and rules of procedure; and they, 
so far as their treatment is of any use, may be more con- 
veniently dispersed over the single sections than gathered to- 
gether into a special part. Cf. § 5. 

These criticisms of details by no means prevent us from 
recognising that Schleiermacher’s fundamental dialectical prin- 
ciples in general point to the direction in which the true 
mean is to be sought, between the opposites of the subjec- 
tively formal and the metaphysical Logics. 


§ 34. Ritter and Vorländer follow Schleiermacher ge- 
nerally in his treatment of Logic. Beneke, Trendelen- 
burg, and Lotze, in single essential relations proceed 
upon his fundamental opinions about Logic. Then the 
whole post-Hegelian labours in the province of the doc- 
trine of thought and knowledge, so far as they do not 
belong to any one of the Schools already mentioned, 
occupy a common middle place between the opposites 
of the Subjectively-formal and the Metaphysical Logics. 


Schleiermacher neither founded nor wished to found a phi- 
losophical school in the strict sense of the word. He wished 
to rouse on all sides and waken individuality. His treatises 
and writings are as fitted, by their wealth of ingenious and 
acute thoughts, to quicken and bear fruit on all sides, as they 








§ 34. The Latest German Logteians. 73 





are unfitted, by the absence of a complete systematic form and 
a strict terminology (which Schleiermacher designedly avoided, 
partly from a horror of the danger of dogmatic stiffness), 
to form the uniting symbol of a school. Those of Schleier- 
macher’s philosophical works in which he strove after a stricter 
systematic form were not published until after his death. 
Hence, those Logicians who follow Schleiermacher most 
closely can only be called his scholars in the wider sense that 
they chiefly move within the circle of thoughts awakened 
by him. 

The logical writings of the above-named philosophers are 
the following: Heinr. Ritter, Vorlesungen zur Einleitung in 
die Logik, 1823; Abriss der philosophischen Logik, 1824, 2nd 
ed., 1829; System der Logik und Metaphysik, 1856; Encyclo- 
pädie der philos. Wissenschaften, 1862 ff.— Franz Vorländer, 
Wissenschaft der Erkenntniss, Marburg u. Leipzig, 1847.— 
Ed. Beneke (1798-1854), Erkenntnisslehre in ihren Grund- 
zügen dargelegt, Jena, 1820; Lehrbuch der Logik als Kunst- 
lehre des Denkens, Berlin, 1832; System der Logik als 
Kunstlehre des Denkens, Berlin, 1842.—J. G. Dressler follows 
Beneke, Praktische Denklehre, Bautzen, 1852; Die Grund- 
lehren der Psychologie und Logik, ein Leitfaden zum 
Unterricht in diesen Wissenschaften für höhere Lehranstalten, 
sowie zur Selbstbelehrung, Leipzig, 1867.— Trendelenburg, 
Logische Untersuchungen, Berlin, 1840; 3rd enlarged ed. 
Leipzig, 1870; cf. Karl. Aug. Jul. Hoffmann, Abriss der 
Logik fiir den Gymnasialunterricht, Clausthal, 1859 ; 2nd ed., 
1868.—Rud. Herm. Lotze, Logik, Leipzig, 1843. 

We may further mention in this place some logical writings 
which, when the one is compared with the other, have very 
various characters, but have this at least in common, that 
they belong neither to the pure subjectivism of the Kantian 
Logic, nor yet to the Hegelian identification of thinking and 
being, but seek an intermediate direction: —Jul. Braniss 
(inspired by Schleiermacher and by Steffens, the friend of 
Schelling), Die Logik in ihrem Verhältnisse zur Philosophie 
geschichtlich betrachtet, 1823 ; Grundriss der Logik, 1830.— 











74 § 35. Modern Logicians beyond Germany. 





Imm. Herm. Fichte (b. 1797), Grundziige zum System der 
Philosophie, Part I., Das Erkennen als Selbsterkennen, Hei- 
delberg, 1833.— Bernh. Bolzano, W issenschaftslehre, Salshäch 
1837.—H. M. Chalybäus (1792-1862), Winenschefieliies, 
Kiel, 1846; Fundamentalphilosophie, Kiel, 1061. Meraaien 
Ulrici (b. 1806), System der Logik, Leipzig, 1852; Com- 
pendium der Logik, Leipzig, 1860 (Ulrici treats of oui 
thought only in this work).—Martin Katzenberger, Grund- 
fragen der Logik, Leipzig, 1858.—J. Sengler, Eikenntains: 
lehre, Heidelberg, 1858.— Ernst Ferd. Friedrich, Beiträre 
zur Forderung der Logik, Noétik und Wissteashafuldire 
(i.e. upon the ‘science the rational existence of things, the 
theory of thinking, and the doctrine of evidence " or 
the ‘Metaphysic, Formal, and Inductive Logic’) wil Ϊ 
Leipzig, 1864.—J. H. v. Kirchmann, Die Plühsiehie ‘des 
Wissens, vol. i., Berlin, 1864.—Rud. Seydel, Logik oder Wis- 
senschaft vom Wissen, Leipzig, 1800. Filh, Hoscnkrunte 
Die Wissenschaft des Wissens, München, 1866-69. In the 
Aristotelian-Scholastic sense, yet with reference to modern 
enquiries, Georg Hagemann, Logik und Noétik, Münster 
1868.—L. Rabus, Logik und Metaphysik, I. Eıkenutaies- 
theorie, Geschichte der Logik, Syst. der Logik, Erlangen 
1868 (1867).—J. Hoppe, Die gesammte Logik, er 
1868 (1867).—Many articles in the philosophical PR 
edited by J. H. Fichte, Ulrici, and Wirth, by Allihn and 
Ziller, and by Michelet and Bergmann, refer to the debated 
questions about the general character, and about single μὰς 
blems of Logic. Karl Alexander von Reichlin- Meldeyg Series 
der Logik, nebst Enleitung in der Philosophie Was 1870 
appeared quite recently. : 
The general reference to their works will suffice for the 
logical labours of the philosophers named here, as they belon 
not so much to history as‘to the present. , τ ᾿ 


| $ 35. Recent German speculation has had in general 
little influence upon logical studies beyond Germany 
The theory of Induction, especially in its application to 








ns beyond Germany. 


§ 35. Modern Logicia 


natural science, has been advanced by Comte, J. Her- 


schel, Whewell, and Mill. 


Among logieians who have kept to the old ways of regard- 
ing the science may be named :—(Archbishop) Whately, Ele- 
ments of Logic, 9th ed. 1868, London ;—Karslake, Aid 
to the Study of Logic, Oxford, 1851 ——J. L. Balmes (pres- 
bytero), El Criterio, Barcelona, 1845 ; Curso de Filosofia 
elemental (Logica, Metafisica, Etica, Historia de la Filosofia), 
Madrid, 1837, Barcelona, 1847, Paris, 1851, translated into 
German by F. Lorinser, Regensburg, 1852. 

Garelli, Della Logica, o Teoria della Scienza, 2nd ed. 
Torino, 1859. J. G. Ulber, Logica, ossia Teoria del Pensiero, 
Napoli, 1863. 

The following have been influenced by the Kantian doctrine 
of knowledge :—A. Tandel, Cours de Logique, Liege, 1844 ;— 

W. Whewell, The Philosophy of the Inductive Sciences, 
founded upon the History of the Physical Sciences, London, 
1840, 2nd ed. 1847, “γᾷ ed. 1857; cf. his History of the 
Inductive Sciences, 1837, translated into German by Littrow, 
1839-42 ;—Henry Longueville Mansel, Prolegomena Logica, 
an Inquiry into the Psychological Character of Logical Pro- 
cesses, Oxford, 1851, London, 1861; Artis Log. Rudimenta, 
Ind ed., Oxford, 1852 ——W. Thomson, An Outline of the 
Necessary Laws of Thought, 3rd ed., London, 1852 ;— Sir W. 
Hamilton, Discussions on Philosophy and Literature, 1852, 
2nd ed. 1869; Lectures on Logic, edited by H. L. Mansel 

and J. Veitch, Edinburgh, 1859, 2nd ed. 1869;—A. C. 

Fraser, Rational Philosophy in History and System, Edin- 

burgh, 1857. 

The Logic of Chance—an Essay on the Foundations and 
‘nce of the Theory of Probability, with especial reference 


Prov 
to Moral and Social Science, London and 


to its Applications 
Cambridge, 1866. 

The following profess a strict Empiricism :—— Sir John 
Herschel, A Preliminary Discourse on the Study of Natural 


Philosophy, London, 1831 ; of. his review of the works of Dr. 

















76 §35. Modern Logicians beyond Germany. 





Whewell in the Quarterly Review, June, 1841 ;—John Stuart 
Mill, A System of Logic, Rationative and Inductive, 7th ed. 
1868, London, translated into German by J. Schiel, 2nd ed. 
from the 5th ed. of the original, Braunschweig, 1862-63 ; 
cf. Die Methode der inductiven Forschung als die Methode 
der Naturforschung, in gedrängter Darstellung, hauptsäch- 
lich nach John Stuart Mill, by J. Schiel, Braunschweig, 1865.! 

C. W. Opzoomer inclines to Empiricism in another sense, De 
Waarheid en hare Kenbronnen, 2nd ed., Leyden, 1863; Het 
Wezen der Kennis, een Leesboek der Logika, Amsterdam, 
1863; cf. his Die Methode der Wissenschaft, ein Handbuch 
der Logik, from the Dutch by G. Schwindt, Utrecht, 1852. 

In France, ‘ Positivism,’ based on the investigation of 
nature and on Mathematics, is represented by A. Comte, 
Cours de Philosophie positive, Paris, 1830-42. 

The principal part of the contents of the work of E. 
Vacherot, La Métaphysique et la Science, Paris, 1858, 2nd 
ed. 1863, belongs to the theory of knowledge; also J. Tissot’s 
Essai de Logique objective, ou Théorie de la connaissance de 
la vérité et de la certitude, Dijon, 1867. J. M. C. Duhamel 
treats of the doctrine of Method in his Des Méthodes dans 
les sciences du raisonnement, Paris, 1865. 

Ch. Waddington, Essai de Logique; Legons faites ἃ la 
Sorbonne de 1848 ἃ 1856, Paris, 1858; and Pellissier, Précis 
dun cours élémentaire de Logique d’aprés les programmes 
officiels de 1857, 2nd ed., Paris, 1860. 5 

Logicians who, seeking a mean between Kant and Hegel 
apprehend Logic to be the science of rules, which hen 
followed enable one to attain to science, i.e. to knowledge con- 
formable to things, are represented by Joseph Delbauf, Pro- 
légoménes philosophique de la Geometrie, Liege, 1860; and 
Essai de Logique scientifique, Prolégoménes, Liege, 1865. 
His doctrines in many considerations approach the method 
pursued in this work. 


; [A fuller account of the recent history of Logic in England will be 
given in Appendix A.] 





§ 36. Definition of Perception. 





PART FIRST. 


PERCEPTION IN ITS RELATION TO OBJECTIVE 
EXISTENCE IN SPACE AND TIME. 


$ 36. Perceprion is the immediate knowledge of things / 
existing together and in succession. Outer or sense- 
perception has to do with the outer world, inner or 
psychological perception with the mental (psychic) life. 


Perception is the first and most immediate form of know- 
ledge, because in it the relation of subject to object rests on 
given natural relations. It thus presupposes no other forms 
of knowledge, but is the foundation of all others, and is con- 
ditioned only by the presence of its object. The mental 
(geistige) element in it is connected in the closest way with 
the definite constitution of nature, and this connection is the 
earlier form according to the universal law of the development 
of spirit. Yet the immediateness of knowledge in percep- 
tion is relative, since many influencing mental (geistige) 
operations are blended in it with the sense-activity, although 
only their collective product appears in consciousness, and not 
they themselves individually. [If this distinction had been 
as clearly stated by Hamilton, he might have escaped. the 
charge of inconsistency which J. S. Mill and J. H. Stirling 


advanced against his doctrine of perception." | 
Perception is distinguished from mere Sensation, which can 


[! Cf. Mill’s Examination of Sir W. Hamilton's Philos. 3rd ed. 
Lond. 1867, p. 17 ff.; Stirling’s Philosophy of Perception, p. 2 ff. ] 











78 § 36. Definition of Perception. 





be more particularly treated in Psychology, by this, that in 
sensation consciousness clings to the subjective occasion merely, 
while in perception it goes out upon something which has been 
perceived, and which therefore, whether it belongs tg the 
outer world or to the subject itself, opposes itself to the 
act of perception as something objective.’ Its (relative) 
immediateness distinguishes perception from thinking which 
produces mediate knowledge, separates perceptions into their 
elements, and re-combines them with each other. Thinking, 
however, may be taken in a wider sense, and understood 
to mean the totality of the (theoretic) functions, which aim 
at the representation of any object in our consciousness. In 
this case perception itself may be called a kind of thinking. 

Perception is the object of Psychology in reference to the 
way it happens, but with regard to the agreement or want of 
agreement of its contents with nature, it is the object of 
Logic. The logical theory of perception is an integral part of 
Logic, the doctrine of knowledge, and not a ‘mere psycho- 
logical introduction’ to the representation of the normative 
laws of the operations of thought. 

There is no contradiction in believing that the laws of percep- 
tion and thought are conditioned by things-in-themselves, and 
that our understanding of the laws of perception and thought 
is conditioned by our scientific knowledge of those things in 
themselves. The opinions of some writers [e.g. Prof. Bain | 
that there is such a contradiction arises from the erroneous sup- 
position that in order to know the thing-in-itself, ἐξ must be in 
our consciousness. The external thing-in-itself cannot be in us, 
but a knowledge of it on which we may depend can be in us. 
We get this knowledge by reflecting upon perception and 
upon thought itself, and in this way can reason back from the 
results to the cause. There is no contradiction in the asser- 
‘tion that a true knowledge of what is outside my conscious- 
ness may be in my consciousness. 


[! Cf. Hamilton, Lect. on Metaph. ii. 93; his edition of Reid's 
Works, p. 876 ff.] 


§ 37. External or Sense-Perception. 








A.—ExTERNAL OR SENSE-PERCEPTION. 


§ 37. The special question of Logic as the doctrine of 


knowledge, is, Whether in sense-perception things appear 


to us as they actually exist, or as they are in themselves? 
Skeptics assert the negative. Their arguments are: The 
agreement of thought with existence, even if there 
were such a thing, could never be known, for the sense- 
perception can only becompared with other perceptions, 
never with its object. The doubt is strengthened when 
we reflect upon the essential nature of sense-perception. 
The perception as an act of the mind (Seele) must either 
be of a purely subjective origin, or at least include a 
subjective element. In either case the assertion that 
the mind reflects undistortedly and exhaustively the 
peculiar real being of what is perceived, can only be 
supported by artificial hypotheses which are difficult 
to be confirmed. The constitution of the world of 
phenomena is at least partly conditioned by the sub- 
jective nature of our sense. Sense may be different in 
other beings, and so may produce other kinds of worlds 
of sense-phenomena. What actually exists as such, as 
it is in itself independent of any way of apprehending 
it, or the thing-in-itself, is different from all of these. 


The uncertainty of sense-perception was maintained by the 
Eleatics, in a certain degree by Demokritus and other natural 
philosophers, then by Plato, and with new arguments by the 
earlier Skeptics. The Stoical criterion, the φαντασία καταληπ- 
τική, was a superfluous assertion, which could not overcome Skep- 
ticism. Among modern philosophers who take up the position 
that sense-perception cannot impart, at least, full material 





80 § 38. Lucorrectness of the Kantian Separation 





truth, we may mention specially, Des Cartes,! Locke (with 
regard to the secondary qualities), Kant,? Herbart,? and 
Beneke* Jos. Delbeuf has discussed afresh the questions 
which belong to the inability to compare the conception with 
its object? He uses the formula: A =f (a, x)—that is, 
the real result, A, is not known as such, but must be brought 
about by a, that is, the object-phenomenon, and x, that is, the 
nature of our mind (Geist). 

[Sir W. Hamilton’s explanation is not unlike Delbeuf’s— 
‘ Suppose that the total object of consciousness in perception is 
= 12, and that the external reality contributes 6, the material 
sense 3, and the mind 3: this may enable you to form some 
rude conjecture of the nature of the object of perception.’ 5] 


§ 38. The Subjective element in sense-perception can- 
not be separated from the Objective in this way, that 
space and time can be referred to the subject only, 
and what fills space and time, or its material (colour, 
sound, &c.), to external things affecting our senses. 
For on this presupposition, although it would be neces- 
sary to apprehend the matter of sense-perception in any 
form of space and time, each particular matter would 
not be referred back to each particular form, and, 
consequently, might be perceived in another form from 
. that in which it actually appears, without having un- 
dergone any real change. But in perception we feel 
ourselves actually confined to the union of definite 
forms with definite matters. Again, modern physics 


1 Meditat. init. 

2 Kritik der r. Vern.; Elementarlehre, Pt.1.; Transcendentalen Aes- 
thetik; and Logik, ed. by Jiische, p. 69 f. 

3 Einl. in die Philosophie, ὃ 19 ff. 

4 Metaphystk, pp. 91-119. 

5 Log. pp. 35 ff., 71 ff., 93 ff.; 105. 

6 [ Lect. on Metaphysics, ii. lect. xxv. p. 129. ] 





of the Matter and Form of Perception. δὲ 


and physiology, because they trace sound, warmth, and 
colour back to the perception of vibrations of air and 
of aether, smell and taste to the perception of certain 
motions connected with chemical occurrences, prove 
the dependence of the content of perception on motions, 
i.e. on changes belonging to the forms of space and 
time. It involves a contradiction therefore to admit that 
content rests on affections which come from without, 
and to believe that these forms nevertheless are derived 
from the perceiving subject only, and are not conditi- 


oned by the external world affecting us. 


The view here combated is that which Aant enunciated 
(Kritik ἃ. r. Vernunft, Part I., Transcendentale Aesthetik). 
The truth that a subjective and an objective element is to 
be distinguished in perception was applied in a very unfor- 
tunate and misleading way, when Kant called the former 
element the form and the latter the content or matter of per- 
ception, and still further defined the form to be intuition of 
space and time. According to Kant, the qualities of sensation, 
such as blue, green, sweet, &c., as such, are only subjective, 
but rest on determinate outward affections, which determine 
the peculiar nature and character of each. This doctrine 
(which was afterwards developed by Joh. Müller into that of 
special sense-energies) is correct enough. The form of intui- 
tion-in-space-and-time, on the other hand, is something purely 
subjective, because ἃ priori; but it is quite inadmissible not 
to attribute to intuition-in-space at least a measure of the 
objective conditionality, which is attributed to the sense- 
qualities, which, as Physics show, depend upon distinct motions. 
Kant’s doctrine of the forms of intuition-in-space-and-time 
wavers. For, on the one side (on the side on which our state- 
ment given above rests), these forms even in their particular 
determinations must originate in the subject only, which can 


G 








82 § 38. /meorrectness of the Kantian Separation, ete. 


only impose on a chaotic matter its ἃ priori forms and laws ; 
and, on the other side, the particular determinate forms and 
the special natural laws must be given empirically, and their 
determinate nature and character cannot in each case grow 
out of the subject alone. They must depend upon the way 
in which the subject is each time affected from the side of 
‘ things-in-themsel ves,’ according to their own peculiar con- 
struction.' 

Fichte, seeing the separation to be untenable, explained both 
the matter and the form of perception to be merely subjective ; 
Schelling and Hegel made it at the same time subjective and 
objective. Herbart subjects the Kantian opinion to a very 
thorough criticism.* 

[Sir W. Hamilton and his School have devoted much labour 
to distinguish the formal from the empirical elements in sense- 
perception. The formal element is called the primary qualities 
of matter, the empirical the secondary. The primary qualities 
are attributes of body as body, are thought of as essential 
to body, and are conceived as modes of a not-self. The 
secondary are attributes of body as this or that kind of body. 
They are thought of as accidental, and are conceived as 
modes of self in relation to bodies. Hamilton has also 


1 For a criticism of the Kantian doctrine, cf. my Grund. der Gesch. 
d. Phil. iii. § 16, 2nd. ed. 

2 Einl. in die Philosophie, ὃ 127; Psychol. als Wissenschaft, in 
Herb. Sämmtlichen Werken, v. 504 ff. Upon the stimuli of sense 
as vibrations in matter, see especially Joh. Müller, Physiologie, 4th ed. 
i. 667 ff., ii. 249 ff. [English translation by Daly, i. 613 ff., 1]. 
903 ff., 1842; Carpenter, Principles of Human Physiology, 7th ed. 
663-722]; cf. George, Die Fünf Sinne, pp. 27-42 ; Maximilian Jacobi, 
Natur- und Geistesleben, pp. 1-04 ; Lotze, Medicinische Psychologie, 
p- 174 ff., 1852; Mikrokosmus, i. 376, 1869; Helmholtz, Ueber die 
Natur der menschlichen Sinnesempfindungen, p. 20 ff., 1852 (where the 
distinction between the sensations and the relations of vibrations is 
emphasised, and the senses are ‘thanked’ very rightly for ‘conjur- 
ing’ out of these vibrations, colours, sounds, &c., and for bringing us 
intelligence of the outer world by these sensations, as if by ‘symbols’) ; 
Ueber das Sehen des Menschen, Leipzig, 18009. 














2 4 
J 


\ 39. Lusufficeency of Sense-Perception. 


secundo-primary qualities, which are intermediate between the 
other two.! 

Mr. Mill and his School ‘ do not think it necessary to ascribe 
to the mind (either in perception or in any other cognitive 
faculty) certain innate forms, in which objects are, as it were, 
moulded into these appearances, but hold that Place, Exten- 
sion, Substance, Cause, and the rest, are conceptions put 
together out of ideas of sensation by the kuown laws of associ- 
tion.’ ?] 


$ 39. Neither the proportion which the external 
reality contributes to the generation of perceptions, nor 
even the eaistence of the object affecting us, can be 
known from the ground of sense-perception alone. 
Perceptions are acts of our mind, and as such do not 
carry us beyond ourselves. The conviction of the 
existence of external objects which affect us depends 
upon the presupposition of causal relations which do 
not belong to sense-perception only. 


The doctrine of Common Sense of the Scottish School (Reid, 
Stewart, Beattie, &c.), as well as the allied doctrine of F. 
H. Jacobi, which asserts that a faith which cannot be scientifi- 
cally explained reveals to us the existence of an external 
world, is a fiction which has no foundation. 

The problem stated in this section can only be settled below 
(in $$ 41-44). 

’ 

[! Cf. Hamilton’s ed. of Reid's Works, Appendix, Note D, pp. 325-75 ; 
cf. Mansel’s Metaphysics, p. 105 ff., 1860; cf. also, for remarks upon 
the same distinction in Bacon's philosophy, the general Preface to his 
philosophical works, by James Spedding and R. L. Ellis, i. 29. Cf also 
Berkeley’s Works, Fraser's Ed. i. pp. 122 ff., 160 ff, 249 ff, and 
passim. 

2 Cf. Mill’s Exam. of Sir W. Hamilton’s Philos. pp. 219 ff., 258 ff., 
3rd ed. 1867; Bain’s Senses and Intellect passim ; Deductive Logic, 
p- 10. ] 











84 40. Agreement of the Inner Perception 


B.—InrerRNAL OR PSYCHOLOGICAL PERCEPTION. 


§ 40. Internal Perception, or the immediate knowledge of 
mental (psychic) acts and constructions, can apprehend 
its objects as they are ın themselves with material truth. 
For internal perception results when the individual pro- 
duction is apprehended by means of the process of Asso- 
ciation as an integral part of our whole mental produc- 
tion. It reaches its most developed form, blended with 
thought, when the mental production under considera- 
tion is placed under the notion to which it refers, and 
when at the same time the consciousness, which he who 
performs the internal perception has of himself, has 
reached the form expressed by ‘Ego.’ But: (a) The as- 
sociation of a single act with others cannot change its con- 
tent and form. It remains what it is. We are conscious 
of our present conceptions, thoughts, feelings, desires, 
and in general of the elements of our mental (psychic) 
life, and of their mutual relations as they actually exist ; 
and they actually exist as we are conscious of them. 
In mental acts, consciousness and existence are one and 
the same. (b) In the recollection of earlier mental acts, 
their thought-pictures, remaining in unconsciousness, 
are again aroused. Larlier acts may be reproduced, 
with less intensity it is true, but in actual agree- 
ment with their original existence. (c) By the sub- 
sumption of individual acts and productions under the 
corresponding general notion, the strength of conscious- 
ness is directed to their common character, without the 
admixture of any foreign element. The consciousness 
attained by this of our mental acts. and productions 








with the Perceived Realty. 85 











naturally harmonises with the real existence of these 
elements. But the possibility of error increases as we, 
in order to determine its notion, go beyond the act itself, 
and consider its genesis and relations (e.g. as in the ques- 


tion whether a certain conception be a perception or an 
illusion). (d) Self-consciousness in the strict sense, or 
consciousness of the Ego, deveiopes itself in three mo- 
ments. The first moment is the unity of an individual 
‚apable of consciousness, by means of which every par- 
ticular in it must be viewed not as an independent 
existence, which together with others is found in an 
accidental aggregate, but as a member of a single 
whole organism. The second moment is the conscious- 
ness which the individual has of itself as one indivi- 
dual, or the coherent perception of single mental acts and 
productions in their mutual combinations, according to 
which they belong collectively to the same being. The 
third moment is the further perception, that that con- 
sciousness which the individual has of itself as an indi- 
vidual belongs again to the same being as the acts and 
productions to which it is directed,—in other words, the 
perception that the being conceived and conceiving, or 
the object and the subject of the conception, is one and 
the same. The first and second moments constitute the 
presuppositions or foundations; the third constitutes 
the essence of the self-consciousness as consciousness of 
the Ego. This moment is only an inner perception 
become potential, and so does not introduce anything 
different from the actual existence. Accordingly, in 
every form of internal perception directed to one’s own 
mental life, and in every form of thought combining 

















86 $40. Agreement of the Inner Perception 


with it and working it up in internal experience, the 
phenomenon is in essential agreement with the mental 


actual existence. 


That my pain appears to me as my pain, my sensation of colour 
as my sensation of colour, &c. is self-evident, and to wish to 
prove this were quite superfluous. But the psychological 
transcendentalist would distinguish from the pain, from the 
sensation of sound or of colour, (not only the essence and 
substance of. the soul, and the inner conditions of individual 
mental occurrence, and not only the outer affections inducing 
them, with all of which the present investigation has nothing 
to do—but also) an existence in-itself even of those psycho- 
logical modifications in me, which appear to me as pain, sen- 
sation of colour, sound, &e. The present argument aims at 
proving the incorrectness of this distinction. I perceive by 
sense-perception a sound, a colour, &c. correctly, in the em- 
pirical sense, if I perceive it as it must be perceived by the 
normal sense-perception. I remember rightly when my me- 
mory-conception corresponds with this normal perception. 
Yet the question ever arises, whether this normal perception 
agrees with the fact as it took place in itself outside my con- 
sciousness, and, by working on my sense, gave rise to my per- 
ception. This question is, however, meaningless when it refers 
to the psychological apprehension of one of my sensations or of 
any of my mental productions. The distin;.on of truth in the 
< empirical ’ and in the ‘ transcendental’ sense which is valid of 
sense-perception can only be applied by a false analogy to in- 
ternal perception. There is meaning not only in seeking to 
know what are the external, but also what are the internal con- 
ditions of the origin of a mental act; but when the mental image 
as such is the object of my apprehension, there is no meaning 
in seeking to distinguish its existence in my consciousness (in 
me) from its existence out of my consciousness (in itself)— 
for the object apprehended is, in this case, one which does not 
even exist, as the objects of external perception do, in itself 
outside my consciousness. It exists only within me. In the 


with the Perceived Realty. 87 
external perception the sensation of the subject contains not 
only elements which correspond with objective existence, but 
also elements which differ from it; and these last, the 
subjective elements, make a discrepancy between the image 
and the objective reality. In internal perception, on the other 
hand, so far as this has to do with my own acts immediately 
present in my consciousness (unless memory requires to come 
forward to introduce them), the subjective action, because it is 
itself the object of the apprehension, cannot, as purely sub- 
jective, contain elements which establish an inconsistency with 
the object to be apprehended. Every subject in this self- 
apprehension is also object. We have not to distinguish be- 
tween two things which might or might not correspond with 
each other. There is only one thing identical with itself. The 
question of agreement, of course, enters into the conceptions 
of memory, and the subsumption of mental productions under 
psychological notions. The relation is no longer that of iden- 
tity; but what apprehends can be homogeneous with what is 
to be apprehended, for both belong to the same animate exist- 
ence. It cannot be presumed to be so in sense-perception ; 
for there, what apprehends is mind, and what is apprehended 
belongs to the external world. 

To understand the nature of self-consciousness one must not 
confound the identity of the conceiving with the conceived 
essence, or the identity of the person with a supposed identity 
of the act of self-conception with the acts and productions to 
which the self-conception is directed. Nor must one, with 
Hegel, confound the identity of the person, as the concrete unity 
embracing in itself all acts, with the pretended identity of a 
supposed monad reduced to a simple quality which remains 
over after the abstraction of all actual acts. If we call the 
totality of these mental elements (conceptions, feelings, desires, 
&c.), to which the internal perception is directed, A, and the 
inner perception itself B, then B is not identical with A (how- 
ever much correspondent), it is only very closely associated. 
But the essence to which both belong, as integral parts, is 
identical, or one and the same essence. That B is only the 








88 § 40. Agreement of the Inner Perception 





consciousness of the singularity of itself as a person, which 
consciousness is expressed in language by naming one’s proper 
name. Self-consciousness, however, as consciousness of the 
Ego, ©, is the consciousness of the co-existence of A and B 
in one and the same essence, the Ego, which includes in itself 
the totality of all my mental acts. 

The objection quoted in § 3, and § 37, against the possibility 
of truth and of the certainty of truth in the material sense, 
because a comparison of our conceptions with existence is 
never possible, but only their comparison with other concep- 
tions, does not find application to what has been said about 
the internal perception of our mental acts and productions. 
We take to ourselves only an uncertain picture of material ex- 
ternal things. We picture within ourselves in a more adequate 
form the thoughts, feelings, and volitions of others. Still more, 
memory may be Zrue to my own earlier received thoughts, to 
my own feelings and volitions. The immediate apprehension 
of the mental images immediately presented to me is necessarily 
true. Error is possible only when they are subsumed under a 
general notion. In this sense, internal perception, more trust- 
worthy than external,is the foundation of all philosophical know- 
ledge. ‘That we have a perception of our own inner mental 
(psychic) life, into which existence immediately enters, without 
the admixture of a foreign form, is the first stronghold of the 
theory of knowledge. 

Melissus the Eleatic asked: ‘ If nothing existed, how could 
men speak as of something?’ The certainty of the existence 
of speech (and therefore also of thought) was to him the 
prius. The certainty of the thought of his own existence lies 
at the bottom of all the utterances of Parmenides about thought. 
After the subjective individualism of Protagoras had iden- 
tified appearance and existence, Aristippus sisted upon the 
subjective truth of sensations. We only know that outer 
things which work upon us by the affections, exist, not 
how they exist; but sensation itself is in our consciousness.! 


I τὸ πάθος ἡμῖν ἐστι φαινόμενον, Aristippus in Sext. Emp. adv. Math. 


vii. 91. 























with the Perceived Reality. 89 
The Socratic study of Ethics and the church doctrine of 
Salvation made men look to the inner life. Augustine re- 
cognised that the conception which we have of external things 
may deceive us, but that the consciousness by the spirit of 
its own life, memory, thought, and volition, is free from de- 
ception. In this sense he puts forward the claim (De Vera 
Religione, pp. 39,72): ‘ Noli foras ire, in te redi, in interiore 
homine habitat veritas (et si animam mutabilem inveneris, trans- 
scende te ipsum).’ Cf. contra Academicos, iii. 26: noli plus 
assentiri, quam ut ita tibi apparere persuadeas, et nulla de- 
ceptio est. Soliloqu. ii. 1: tu qui vis te nosse, scis esse te? 
scio; unde scis? nescio; simplicem te scis an multiplicem ? 
nescio; moveri te scis? nescio; cogitare te scis? scio. De 
Trinitate, x. 14: si dubitat, vivit; si dubitat, unde dubitet, 
meminit ; si dubitat, dubitare se intellegit; si dubitat, certus 
esse vult; si dubitat, cogitat; si dubitat, scit se nescire; si 
dubitat, iudicat non se temere consentire oportere. Cf. de Civ. 
Dei, xi. 26. 

So also, in the Middle Ages, Occam the Nominalist taught 
that the propositions, such as, I know that I live, think, &c. 
are surer than sense-perceptions. 

Des Cartes, however, was the first to found a system of 
philosophy on this principle. Thought (cogitare) is to him 
the most certain of all things ; but ‘ under thought,’ he explains, 
‘I include all that enters into our consciousness, so far as we 


are conscious of it, and so volitions, conceptions, and sensa- 
tions.”! 


Kant, on the other hand, disputes the truth of self-know- 
ledge also. Development in time belongs to our existence, not 
actually as it is in itself, but only as it is phenomenal; and 
this development in time depends upon this, that the ‘ internal 
sense ’ is accompanied by the intuitional form of time. Our true 
being remains completely unknown to us. But if there were 
an inner sense of such a kind as Kant imagined, so that, when 
our being, in itself timeless, affected it, then the phenomenon 
of our conscious life in time resulted, this would yet be a result 


"1 AMeédit. ii. ; Princ. phil. i. 9. 








90 κα 40. Agreement of the Inner Perception, ete. 


which has actually happened. Consciousness and existence 
would still be identical in relation to our development Ἢ 
time, and the proposition would remain valid,—our mental 
(psychic) life in time exists in itself as we are conscious of it 
and we are conscious of it as it exists. A stricter EEE TERN 
treatment of the nature of internal perception makes ers 
dent that the Kantian hypothesis about our internal sense is 
untenable. We apprehend also our self-apprehension which 
according to Kant, exists in time. By what “ Inkraa ein 
and by what form does this happen? Internal perception 
cannot bring time into what is in itself timeless, but can only 
recognise that what has already the attribute of time in itself is 
in time. (It is a wholly different question, and one Ιοϊδοων 
not to the doctrine of knowledge but to metaphysics, to ask— 
Has time any independent power or subsistence, or is it only 
an outflow of the essence of things, and in this sense merely 


ε] 


phenomenal? and if so, how far does each thine bear about 
in itself its own measure of time? The confusion of the meta- 
physical opposition between essential existence and what ts out- 
side of essential existence, where the two sides belong to the 
peculiar nature of things, with the opposition in Logic or in the 
doctrine of knowledge between the peculiar existence of things or 
their existence in themselves, and the phenomenon which rs only 
considered to be a true or untrue ın irroring of things, has caused 
unspeakable confusion in these investigations.) 

Hegel makes internal perception, as he makes external. the 
propaedeutical starting-point, not the scientific foundation of 
philosophy, and allows truth to mental (psychic) Deo in 
so far as they make moments in the dialectical self-development 
of the Absolute. | 

Schleiermacher rightly finds in self-consciousness the point 
where thought and being are originally identical: ‘ We exist 
thinking, and we think existing.”? 

Beneke, in agreement with Schleiermacher, teaches, ° All 

a re Encyclopadie, ὃ 413 tt. 

Dial. - p. 90, and Erläut. p. 54 ff.; ef. Beil. D. xviii. xix. 
Ρ. 452 ff., and Beil. 2. xx.-xxiii. 488 ff. 





S41. Plurality of Animate Existences. QI 





knowledge of our mental (psychic) activities is a knowledge of 
an existence in itself, i.e. the knowledge of an existence 
appears as it is in and for itself, or is independent of its being 


conceived,’! and makes this proposition the basis of his doctrine 
of Metaphysics (with him comprehending in itself the doctrine- 
of knowledge).? | 

[Hamilton distinguishes carefully ‘between the data or 
deliverances of consciousness considered simply iz themselves, 
as apprehended facts or actual manifestations, and those de- 
liverances considered as testimonies to the truth of facts beyond 
their own phenomenal existence ;’ but in so doing neither sufh- 
ciently distinguishes the state of the case in external perception 
from that in internal perception, nor sets clearly before himself 
the difference between the logical and metaphysical problems.?] 


C.—THE CoMBINATION OF INTERNAL AND EXTERNAL 
PERCEPTION. 


$ 41. The knowledge of the outer world depends upon 


the combination of external with internal perception. Our 
corporeal circumstances, sensibly perceived by ourselves, 
are in orderly coherence with circumstances belonging 


to our internal perception. In consequence of this co- 


herence, that association grows up within us, by means 

of which we presuppose, along with the sense-perception 

of corporeal circumstances analogous to our own, ἃ 

mental (psychic) existence also analogous. This combina- 

tion, which is at first carried on instinctively, as it were, 

without any conscious reflection upon the mental laws 
I Neue Grundlegung zur Metaphysik, p. 10, 1822. 


2 System der Metaphysik, pp. 68-75, 1840; Lehrbuch der Psychol. 
§ 129, p. 121, 1845; cf. W. F. Volkmann, Grundriss der Psychologie, 


Halle, p. 169, 1856. "- 
3 [Cf. Hamilton’s ed. of Reid’s Works, p. 743 ff.; Lect. i. 138; cf. 


Mill’s Exam. of Sir W. Hamilton’s Philosophy, 3rd ed. pp. 234—43.] 




















S 41]. Plurahty of Animate Existences. 








of logical development, if logically developed, takes the 
form of a reasoning from analogy—as our corporeal phe- 
nomena are to our mental reality, so other corporeal phe- 
nomena are to a strange mental reality (here accord- 
As to the logical correctness of the 
presupposition of a plurality of personal essences after 


ingly presupposed). 


the analogy of our own existence, it is generally un- 
doubtedly certain, that, by this combination of the con- 
tent of external perception with that of internal, we 
make the first a moment, which belongs to reality, 
although it does not present itself in the external sense 
according to its nature. The proof for this lies partly 
in the consciousness, that the species and connection of 
external phenomena under consideration are not wholly 
conditioned by the mere causality of our own individual 
mental (psychic) life, partly in the thorough-going 
positive confirmation which the presupposition has from 
experience. 

It does not belong to Logic to explain further the psycho- 
logical side of this matter. Logic has to do with what is 
psychological only in the form of an hypothesis to be established 
in some other place. On the other hand, it does belong to 
Logic to prove the logical right, or to decide upon the ques- 
tion, whether the assertion originally and necessarily formed 


according to psychological laws has truth, 1.6. agreement with 
existence. This follows from the general notion of both sciences. 
See $$ 2, 6, and 36. 

Schleiermacher was the first to recognise correctly that in the 
knowledge of existence external to us we first affirm a plurality 
of animate subjects. Beneke follows him in this, but expresses 
the psychological relation more definitely. He finds in it the 
essential foundation of Metaphysics.! 


' Grundleg. der Metaphys. p. 23; Syst. der Metaphys. pp. 76-90; 





\ 42. The Gradual Series of Existences, ete. 93 





$ 42. Extending his consideration of the external 
world, man recognises the internal characters of other 
things, chiefly by means of the related sides of his own, 
inner existence. He copies in himself the existence of 
higher and lower objects; for he partly raises, partly 
lowers, the corresponding moments of his own mind, 
and in this fashion gives a supplementary meaning to 
the content of the external perception of what appears 
at the time. By such a reproductive process, developed, 
trained, and fitted for a deeper self-knowledge, he imi- 
tatively seeks to recognise in gradually higher proportion 
the inner nature of other essences. The truth of these 
elements of knowledge modifies itself according to two 
relations: (1) in objective relation according to the 
distance of the then present objects of knowledge from 
our own existence ; (2) in subjective relation accord- 


ing to the discrimination between nearer and more 
remote analogy, and to the suitable application of this 


discrimination to phenomena. 


The foregoing propositions contain the logical principles for 
determining a series of important questions in different spheres 
of real science. In the gradual series of earthly existences the 
law holds good that the higher essence takes up into it the 
character of the lower as a moment.! : The animal, while it is 
raised above the plants by consciousness, contains the vegetative 


Lehrbuch der Psych. 2nd ed. § 159, p. 149 f.; cf. Herbart, Werke, 
v. 187; vi. 501 ἢ 

I This law was perhaps, if the fragments of the writing ascribed to 
Philolaus are genuine (cf. § 11), hinted at symbolically by the Pytha- 
goreans. It was recognised more distinctly by Plato and Aristotle in 
their doctrines of the parts or powers of the Soul. It was raised by 
Schelling to be the principle of his Nature-Philosophy, and determined 
the whole course of the Hegelian Dialectic. 











Ss 


94 ὃ 42. The Gradual Series of Existences— 
powers as the ground in which the peculiar animal life takes 
root; and in the same way man unites in himself, along with 
the activities of reason, the powers of vegetative and animal 
life. By this he is capable of acquiring an approximately true 
judgment of the life of animals, and, with reference to their 
working powers generally, of the essential nature of plants and 
of nature as a whole, since he reflects upon the lower in him- 
self, and reduces its character in his conception to an inferior 
power. A modern searcher into nature says rightly on this 
matter: * As the investigation of nature was originally pro- 
duced by the feeling of the inner kinship of nature with the 
essential being of man, it is also its aim to lay hold of this 
coherence in its whole depth, and bring it to knowledge.’ 
‘ The history of nature gains its highest significance when it 
is connected with the history of the development of man.’! On 
the other side, man apprehends the higher and divine by 
idealising his peculiar inner nature, and that in the form of 
faith and presentiment, since he cannot bring adequate powers 
of knowledge to bear upon it. If one defines the relation of 
faith, in the more general sense, to knowledge as that of nice 
perception (tact) to proof,? then this wider notion of faith in- 
cludes the more special one of immediate trust in a higher Being, 
and the recognition of his authority. This trust must take the 
form of nice perception (tact), because what is lower cannot 
completely copy the higher, and therefore cannot test it (or 
prove it) scientifically. But in proportion as our own mind 
developes by advances in intelligence and morality, and becomes 
higher, the higher without us can be recognised by us in a more 


1 Braun, Betrachtungen über die Verjüngung in der Natur, pt. xi. 
p- 15, 1850. 

2 Tact is the ability to reach a definite result by means of an irre- 
flective combination of manifold elements without clear consciousness 
of the individual members combined. Proof or Analysis brings the 
individual members into consciousness, and separates the true from the 
false. Cf. Beneke, Lehrbuch der Psychologie, § 158; Psych. Skizzen, 
ii. 275 ff.; Syst. der Logik, i. 268 f.; Lazarus, Das Leben der Seele, 
11. 286; ef. N 101. 





Science, Faith, Presentiment, Opinion, ete. 95 


and more adequate way, and faith become scientific knowledge 
or vision. _Hence, within certain Jimits, according to the 
different stages of mental development, the same content of 
knowledge, which is only an object of faith for the one, is for 
others an object of knowledge. But as often as knowledge 
completely annexes to itself one province, a higher province of 
faith reveals itself. It must be noted, with regard to the sub- 
jective criterion or discrimination between nearer and further 
analogy, that the uneducated consciousness is at the same time 
liable to the two opposite faults, of raising the lower too nearly 
up to, and of dragging the higher too nearly down to, its own 
peculiar nature. For, since our own peculiar existence is the 
only one immediately given to us, what first necessarily presents 
itself, until the phenomena refute this first hypothesis, is a 
multiplication of such existences. ‘ Man refers his own pecu- 
liar essence to Nature, and throws into the world of things the 
conception of human relations’ (Trendelenburg). The capa- 
bility both of fully idealising and of in the right way dividing 
and depotentialising our own nature is only attained gradually 
and amidst fluctuations hitherto by no means completely over- 
come even by the sciences. The tendency to anthropomorphism 
does not allow people living in a state of nature either to reach 
the pure ideal above, or the abstract categories of scientific 
physics beneath. It appears in numberless expressions of the 
poets and of the earlier philosophers. The well-known astro- 
nomical axiom of Heraclitus, the ancient equivalent of the 
modern theory of gravitation, belongs to this way of looking at 
things—‘ The sun will not transgress its bounds, for if it did so 
the Furies, the servants of Dike, would find it.’ Timoleon 
erected an altar to Automatia, to the personified might of acci- 
dent, moulding his notion to the very opposite of self-conscious 
personality. The exaltation of Christianity over Judaism 
appeared to the Gnostics to be the exaltation of the God of 
the Christians over the God of the Jews. Clement of Alex- 
andria thought that the Greek philosophy had been given by 
God to men by the lower angels. Up to the present time this 
anthropomorphism continues to exercise its influence, not only 














96 $42. The Gradual Series of Existences, ete. 








in the thousand forms of popular superstition, down to spirit- 
rapping, but also in a way less evident perhaps, but all the 
more prejudicial because it checks the development of the 
sciences, in ‘a course of symbolising myths, which were con- 
sidered real theories,’! and in the hypostatising or quasi-per- 
sonification of the faculties of the soul, of the animal and 
vegetable powers, of the Ideas, and of the Categories, &c. 
Kepler’s Pythagorean theory of heavenly harmony, which 
barred against him the way to Newton’s great discoveries, 
since it did not let him know the actual powers, depends upon 
this way of looking at things, as much as the Ancient and 
Aristotelian-Scholastic personification of the stars or their 
moving principles as gods or angels, 

Auguste Comte, the French philosopher, in his Philosophie 
positive, expresses this relation of personification, mere quasi- 
personification, and adequate description, by the distinction of 
Theology, Metaphysics, and Positive Philosophy ; for he be- 
lieves whole doctrines to embody the logical mistakes which 
explained lightning by an angry Jove, and fire by Phlogiston. 
On the other side, the polemic of science against these childish 
conceptions has not seldom mistaken the limits beyond which 
it becomes unscientific, when it denies the really existing 
analogy, and favours a false dualism. Into this error fell the 
Anaxagorean physics, and still more the Cartesian natural- 
philosophy, which, seeking only pressure and resistance in 
nature, refused recognition to Gravitation and to the animal 
and vegetable powers. The same mistake of scientific endeavour 
induced Spinoza and many others to combat all Teleology, 
true or false. 

Final decision upon all these questions is only possible by 
the help of considerations which belong to the Positive 
Sciences. It belongs to Logic, however, to explain them 
so far as the grounds of determination lie in the essential 
nature of the human power of knowledge in general. A 
Logic which leaves this problem untouched, leaves its task 
unfulfilled in many essential relations. 


I Alex. v. Humboldt, Kosmos, ii. 399; cf. i. 66 ἢ 





N 43. The Reality of Matter and Power. 





That the same and the similar in things are recognised by 
the same and the similar in us is a doctrine agreed upon by 
the ancient Oriental, and by almost all the Greek Philosophers 
except Anazagoras: cf. Arist. De Anima, i. 2,§ 20. In modern 
times the same view comes back in the Leidnizian Monad- 
ology ; in the Kantian view, that the end and aim of Nature 
is the analogue of the moral law; in the theory of Herbart, 
which traces back everything that has ‘really ’ happened, or 
every change of the inner circumstances of a simple real exist- 
ence (monad), to the analogy of conceptions, or of ‘ preserva- 
tions of self’ (Selbsterhaltungen), and to the relations of the 
conceptions of the human mind (Seele); in Schelling’s Nature- 
philosophy ; and in the Hegelian doctrine of the identity of 
thinking and being. Schleiermacher taught that the powers 
of essences in nature were to be looked at as the lower ana- 
logues of the human will, and the whole of nature as a fainter 
Ethic (Dial. p. 150). Man is a mierocosm since he has in 
himself all grades of life, and hence constructs his conceptions 
of the external existence (Dial. p. 109). Schopenhauer forms 
his ‘panthelematism’ on the identification of the notions of 
power and will, but has not sufficiently noticed the distinction 
between a blind impetus and will consciously directed to an 
end. Günther’s ‘dualism’ arises from the thought that the 
analogy between the categories, according to which nature and 
mind (Geist) respectively develope themselves, is not to be 
understood as Identity, but as involving an essential Opposi- 
tion. He was fond of laying stress upon the opposition. 
Beneke has explained in the fullest and most satisfactory way ! 
the problems of the theory of knowledge, which depend on this 
consideration.” 


§ 43. In other phenomena, which cannot be looked 


on as merely subjective because of the consciousness 


' System der Metaph. und Religionsphil. especially pp. 102-5, 
140-438, 495-511. 

> Cf. Trendelenburg, Log. Untersuch. 2nd ed. p.460; 3rd ed. 11.498 f.; 
fist. Beiträge zur Philos. ii. 123-24. 


H 














98 843. The Reality of Matter and Power. 





that they are not merely dependent on our own mental 
causality, the transference of the analogues of our own 
mental (psychic) life, by means of which we know with 
proximate truth the psychic life both of other men and of 
animals, does not seem to hold good. These phenomena 
lead to the admission of a material (Stoff), which we call 
Matter, remaining in itself in dead stillness, and capa- 
ble of change only by outer impulse. But the notion 
of matter so acquired cannot correspond with its actual 
existence. Every phenomenon objectively founded, as 
this very act of becoming a phenomenon itself testifies, 
and as the scientific investigation of the laws of nature 
makes evident, is to be traced back to some active power 
as its real basis. In all matter—and if there are atoms, 
in every atom—there must lie some internal conditions 


or qualities, which if they become mutually related in 
the immediate contact, or in the partial or total inter- 
penetration of matters (Stoffe), become powers by their 
opposition in reference to each other. 


The notions of Matter and Power denote two ways of 
comprehending things; on the one side by sense-perception, on 
the other by the analogy of the internal perception of our 
own power of will. Helmholtz rightly says,' “Matter and 
power are abstractions from the actual; science calls the ob- 
jects of the outer world matter (substance) according to their 
mere existence there, without regard to their effects on other 
objects, or on our organs of sense, but we attribute power 
to them considered as acting. What Herbart taught of the 
qualities of his supposititious point-essences, which he calls 
‘simple real essences,’ holds true of the qualities of extended 
things: they act in contact as powers. 


I Erhaltung der Kraft, p. 4 f., Berlin, 1847. 





§ 44. Reality of Space and Time. 99 





§ 44. The co-existence and co-operation of a multi- 
plicity of powers necessarily involve some real ordér 
of coherence and succession, or some real existence in 
space and in time. This cannot be of a kind different 
from the space and time of sense; for if the reality of 
development in time is recognised ($$ 40-43), then on 
the supposition that such a space of three dimensions as 
mathematics require really exists without our mind, and 
on it alone, the psychical-physiological facts which have 
place in our sense-affections are fully explained by 
natural laws. Therefore the order in space and time be- 
longing to real objects mirrors itself in the order in space 
and time of External and Internal Perception. Sense- 
qualities, however, colours, sounds, &e. are, as such, sub- 
jective only. They are not copies of motions, but are 
regularly and connectedly related to determinate motions 
as their symbols (cf. § 38). 


From the truth of Internal Perception (§ 40) it follows that 
succession in time at least is not a mere phenomenon, but a 
reality.' The reality of extension in space in three dimensions 
follows from the reality of time, and must be ascribed to things- 
in-themselves, and not merely to our apprehension of things. 
For the order in time empirically given in us—the change of 
night and day, the change of the seasons, &c.—is embodied in 


' Ik follows not only that we apprehend the mental occurrence in the 
form of time, but that the mental occurrence itself goes on in us in 
time, and therefore also in other animate beings, and further by analogy 
that there is in real things a succession in time, A ‘fallacy’ occurs 
only in the unjustifiable transference of a ‘form of intuition’ only 
mentally (psychieally) real in us to the external reality; for a sub- 
jective form of intuition could of course refer to ‘an order of things 
quite incomprehensible to us,’ but succession in time is a mental reality 
in us, and inference from us to other essences is logically correct. 


H 2 














100 § 44. Reality of Space and Time. 


— —— .ς..ἢἢἢ- - r 








mathematico-physical laws, which, according to the principles 
of Mechanics, can only exist on the supposition of an external 
space which agrees with the space of sense-perception in all 
essential relations. For our senses are affected at certain times 
by certain things which exist in themselves outside of our con- 
sciousness. The succession of phenomena conditioned by their 
affections is to be explained not by the mere internal connection 
between acts of consciousness, but by the wider connection 
which comprehends both the subject and the things-in-them- 
selves which affect us. The natural laws which belong to this 
connection relate to a space of three dimensions. Newton’s 
law in particular, according to which the intensity of gravity 
for unchanged masses is in inverse ratio to the square of the 
distance, necessarily presupposes a real space of three dimen- 
sions. For in a space of only two dimensions the intensity 
must be inversely proportional to the distance itself; in a space 
of three dimensions, to the square of the distance; and in every 
other space to another function of the distance. For since, on 
the hypothesis of two dimensions, the effect in any given dis- 
tance is distributed on the circumference of the circle whose 
radius is the distance, and since, on the hypothesis of three 
dimensions, the effect is distributed on the surface of the cor- 
responding sphere, and so on; and as the circumferences are to 
each other as the radii, and the superficies of the spheres as 
the quadrates of the radii, therefore the part of the whole effect 
which belongs to every individual point is in each case in the 
inverse ratio.! In all physical phenomena, causes and effects 
are exactly commensurate as soon as they are reduced to motions 
in space, and a clear scientific insight into their real connection 
can be attained. And this justifies the fundamental thought 
of this paragraph, which makes the perception-picture in its 
position in space and time strictly parallel with the existence 
in space and time properly belonging to objective reality.” 


1 As Halley (1656-1742) has shown; cf. my treatise on the funda- 
mental contradiction in the Kantian view. Altpreuss. Monatschrift, 
1869. 

2 In the foregoing argument, a ‘brain really extended in three 


$ 44. Reality of Space and Time. IOI 








The relation of sense-qualities, such as sounds and colours 
(Locke’s ‘secondary qualities’), to vibrations resembles that 


dimensions’ has not been presupposed. What has been already proved 
in the preceding paragraphs—that there is a plurality of real essences, 
that many exist outside of the consciousness of one essence, and that 
these may stand in certain changing relations to each other—serves 
only as a starting-point. The connection among phenomena which are 
in the consciousness of the perceiving essenee—e.g. among astronomical 
events, as they occur in the firmament—is not exclusively conditioned 
by the subjective manner in which they are perceived. It also depends 
upon the way—by no means chaotic, by no means presenting a matter 
(Stoj’) to be set in orderly arrangement a priori by the subject alone in 
each particular—in which it is affected by things lying outside its con- 
sciousness. If now these latter are conformable to other laws which are 
to be understood from space knowable geometrically to the essence per- 
ceiving, this essence would be able to attain toa pure geometry har- 
monious with itself, but could never be able to attain to an applied 
geometry harmonious with itself, nor to a geometrico-physical explana- 
tion adapted to phenomena conditioned by sense-affections. By means 
of the projection of the external into the internal any arrangement 
held objective by the percipient subject would arise, on whose basis 
certain expectations finding confirmation in experience are created. 

But this orderly arrangement, in part conditioned by a conformability 
to law different from the form of the intuition of the subject, would 
not be able to be understood from the peculiar nature of this form of 
intuition, as the decrease of gravity in inverse ratio to the square of the 
distance is from the three dimensions of space. For example, in a 
projection from an objective space which has m + a dimensions into a 
subjective space of m dimensions, every relation of intensity of gravity to 
the distance understandable by the subject would vanish ; and the sub- 

ject confined to this form would construct deceptive laws, since it re- 

ceives as objective the course of nature intuitively perceived by it, but 
cannot fully explain it according to the nature of its phenomenal space. 

Physical phenomena find throughout their most complete explanation in 

the supposition, that things-in-themselves exist in a space of three 

dimensions as we know it. It is at least very doubtful that any other 

supposition could be so brought into agreement with the facts. We have, 

therefore, every ground for believing that our conception of substances 

extended in space in three dimensions does not in some way symbolise 

things which exist in themselves in quite another way, but truly repre- 




















102 $44. Reality of Space and Time. 








of sounds to letters.Y It is a constant relation (in the one case 
following by natural necessity, in the other arbitrary), and 
a sameness of combinations without similarity of elements. 

The sceptical thought (cf. § 37) which asserts that our know- 
ledge of the outer world is impossible, or at least unreliable, 
because it cannot be compared with its objects, is finally over- 
come by this, that the consideration of the causal relation gives 
a sufficient equivalent for the immediate comparison which is 
wanting (just as the mathematical reckoning of distances 
makes up for the want of direct measurement). Des Cartes’ 
proof from the Véracité de Dieu, and Delboeuf’s ? from the 
veracity of our thoughts, are expositions of our faith, not 
strict proofs.? 

It has been already seen that the Kantian Dualism, which 
makes ‘ things-in-themselves’ affecting us the exclusive source 
of the material content of perception, and the subject the 
exclusive source of its form and intuition-in-time and-in- 
space, is untenable. But Fichte’s assertion still remains 
possible, that matter and form have both a purely subjective 
origin. So does the intermediate assertion (which has found 
supporters quite lately) that an element is present in the 


sents things as they actually exist in three dimensions. Our conception 
of things and their motions is, therefore, the result of such ‘ an organisa- 
tion of the situation of our sensations’ as effects the harmony, not dis- 
crepancy of things and their phenomena as to size and form or as to the 
‘primary qualities.’ (Cf. my Grund. der Gesch. der Phil. iii. $ 10.) 
From the impossibility that motion can change itself in consciousness, 
follows the necessity of accepting a latent consciousness, which, aroused 
by definite motions, strengthened by combination and corcentration, 
can arise out of its latency. 

1 (Cf. Berkeley, Theory of Vision, Coll. Works, vol. i., Fraser’s Ed. ; 
cf. also Editor’s preface to the Theory, and Fraser’s Life and Philosophy 
of Berkeley, ch. x. ] 

2 Log. pp. 73-78. 

8 [The same may be said of Sir W. Hamilton’s appeal to the veracity 
cf consciousness (Lect. on Metaph. i. 264 ff.) ; edition of Reid’s Works, 
note A, p. 773 ff.; cf. Mill’s Exam. of Hamilton’s Philos. 3rd ed. 
Ρ. 72 f. | 


$ 44. Realty of Space and Time. 103 





things-in-themselves which, when it affects us, originates in us 
the forms of space and time, but that this element has a 
character essentially different from these forms. The possi- 
bility of such an assertion can be disproved, and the real © 
truth of the forms of space and time can be proved, by reflect- 
ing upon internal perception and its co-operation with external. 
One must not presume to rise above the necessity of this scien- 
tific demonstration by a mere axiom, by which the agreement 
of our forms of intuition with those forms of existence is called 
something immediately certain—a postulate of reason, a neces- 
sity of thought, a something lying in the very notion of 
knowledge (since the validity of this notion, so understood, 
has first to be proved). Such dogmatic axioms, which make 
too comfortable pillows, will always lead back to scepticism 
and critical doctrines which they cannot confute. For example, 
in modern times, Schopenhauer, following Kant, says: ‘ One 
must be forsaken by all the gods to imagine that this visible 
world there outside as it fills space in three dimensions, is com- 
pletely objectively real, and exists as it does without our co- 
operation.’! This is true as regards colour, sound, &c., but as 
regards extension and space it is false. And since we do not 
want for arguments to support our position, we need not care 
much about being forsaken by Schopenhauer’s gods. The 
assertions of students of Nature of the Kantian School that 
the investigation of Nature has to do always and above all 
with phenomena, are to be corrected by what we have said 
above, They are true so far as regards the results of the 
sense-affections, but false as regards their causes. These 
causes, the things-in-themselves, the metaphysical bases of 
phenomena, are themselves objects in space and time. The 
thesis—the world of phenomena accommodates itself to things- 
in-themselves; and the antithesis, it accommodates itself to the 
organs of sense—are both one-sided and half-true. The world 
of phenomena is the common result of the two factors whose 
contributions can and must be adjusted. ‘ Secondary qualities’ 


1 Ueber die vierfache Wurzel des Satzes vom zureichenden Grunde, 
2nd ed. § 21, p. 51. 

















104 § 44. Reality of Space and Time. 





(sound, colour, heat, &c.), as such, are purely subjective; and 
they are symbols of motions. Time and space are both sub- 
jective and objective at the same time. 

Schleiermacher rightly teaches'—‘ Space and time are not 
only conceptions of ours, they are the kind and way in which 
things themselves exist.” ‘ Space is the-being-the-one-outside- 
the-other of existences, Time the-being-the-one-outside-the- 
other of actions.” Schleiermacher further held? that if the 
contents of sense were conditioned by sense alone, there would 
result only a chaotic manifold of impressions. ‘ Organic func- 
tion,’ as such, has to do only with the ‘chaotic material,’ or 
the formless boundless manifold of what fills space and time. 
Schleiermacher distinguishes? perception from organic function. 
He defines the perception to be the unity of the organic and in- 
tellectual function with a preponderance of the organic. In 
thought proper intellectual function prevails, and in intwition 
both functions have equal prominence. Schleiermacher, how- 
ever, has not made clear enough what the intellectual element 
is which enters into perception. If we hold that it is ‘ orderly 
arrangement in space and time,’ we may make our theory 
agree with Schleiermacher’s, and consider it to be its com- 
pletion and more definite statement; but we cannot admit 
that the activity of sense or the ‘ organic function’ has not got 
this orderly arrangement. The senses seize upon all those 
forms of existence, as yet in unsettled unity and in ‘ chaotic’ com- 
mixture, on whose separation the different forms of thought 
rest (e.g. the essential and the non-essential, on whose separa- 
tion depends the formation of the notion; substantiality and 
inherence, which are the basis of the subject: and the pre- 
dicate of the judgment). They do not apprehend chaotically, 
but in distinct separation, those forms which make their 
special object, the relations of existence in space and time, or 
the external arrangement of things, in which the internal dis- 
tinctly expresses itself. The physiological consideration of the 
senses of Sight and Touch shows that the capability to ap- 
prehend distinct positions is established in their organisation. 


| Dial. p. 385 f ὀ Ἃδ Ibid. §§ 108, 118, 185. 3 Ibid. § 115. 


§ 44. Realty of Space and Time. 105 





The eye, it is true, does not see three dimensions ; but mere 
sensation suffices to distinguish positions on a superficies, 6n 
which distinction rests all further discrimination of the actual 
form of what is seen, and is so far by no means chaotic. If 
one believed (with Herbart and Lotze) that all separation in 
space of parts of the organic image of sight and of the affec- 
tions of the nervous vanishes in the spacelessness of the simple 
mental monads, in order to be reproduced in consciousness in a 
new way, out of the quality of sensation in general, or, accord- 
ing to Lotze, out of certain ‘ signs of place,’ even on this hypo- 
thesis (which is not admissible from Schleiermacher’s stand- 
point) it must be recognised that the production of every 
definite position of the picture conceived in space and time 
is conditioned by the position in space and time of each 
organic affection, and this again, on its side, by the position 
of the external thing affecting. The organic function even 
in this case would be by no means chaotic. 

Again, Schleiermacher’s view of the nature of the sense- 
activity may be refuted directly from his own dialectical prin- 
ciples. For Schleiermacher distinguishes, in existence gene- 
rally, ‘ Power’ (Kraft) and ‘ Action, and refers the former to 
existence-for-itself, and the latter to existence in connection 
with others. But the arrangement of real objects affecting 
our senses, and the organic function itself, fall under the notion 
of co-existence and co-operation or of “Action.” The kind 
of this co-operation, however, can only be determined by the 
‘ System of Powers,’ and since, according to Schleiermacher, 
this is known to be undoubtedly conformable to reason, the 
co-operation must also be orderly. Hence organic function 
as ‘The “ Action” of things in us’! is not a chaotic but an 
orderly manifold of impressions. The same thing can also be 
proved indirectly. If the organic function, as such, produces 
a mere chaos of sensations, the function of reason could not 
stand in essential relation to it, but could only come after it, as 
something original and independent of it. Schleiermacher, in 
consequence of this opinion, ascribes to organic function this 


ι Dial. p. 56. 

















106 δ. 44. Reality of Space and Time. 





significance only, that it excites the intellectual to self-activity. 
He thinks that ‘ the system of all notions constituting science 
is given in a timeless way in one reason dwelling in all.’! These 
actual notions are always realised ‘in connection with organic 
function ;** but organic function is not a co-operating factor in 
the formation of notions, it is only an exciting element, on 
occasion of which the notions, lying in the universal reason in 
individuals and in races of men, develope themselves in con- 
sciousness more fully and more purely. Schleiermacher thus 
only allows organic function, as follows from the presup- 
position of its chaotic character, to influence the becoming 
conscious, not the formation and development of notions. But 
then he explains that ‘pure thought’ in the Hegelian sense, 
or the self-sufficiency of intellectual power wholly freed from 
any intermixture with organic function, is impossible. He is 
right, but scarcely consistent; for the impossibility of pure 
thought of any kind contradicts throughout Schleiermacher’s 
presuppositions about organic function, and the system of 
notions. Why should pure thought be impossible if these pre- 
suppositions are true? ‘The mere excitement of intellectual 
activity might as well have happened from some other side 
than that of sense-activity,—from the will or the resolve to 
keep itself thinking, and from the living power of delibera- 
tion. Schleiermacher says, because ‘the activity of the rea- 
son, when it is set up, apart from all activity of the organisa- 
tion, is no longer thinking,’* or, because “apart from all 
organic function no ground of partition can be found for the 
unity of existence.” But this only proves that no system 
of notions can ever be given in the human reason in itself, 
which only needs successive awakening to consciousness; for 
every system of notions presupposes a partition of indeter- 
minate abstract existence. If the doctrine of the impossibility 
of that pure thought, and the corresponding doctrine of the 
impossibility of partitioning the unity of existence into a 
plurality of distinct notions by means of mere intellectual 


1 Dial. p. 104. 2 Ibid. p. 105. 
4 Ibid. § 109, p. 57. 


3 Ibid. p. 106 ff. § 177. 
5 Ibid. § 168, p. 96. 


§ 44. Realty of Space and Time. 107 





function, be held correct, the view of the chaotic character of 
organic function, and the corresponding assertion that the sys- 
tem of notions is given in intellectual function, must be given 
up. The content of perception reached by means of organic 
affection must be recognised to be a co-operating factor in the 
process of the formation of notions. The notion is by no 
means reduced on this view to a ‘merely secondary product of 
the organic function ’—a doctrine Schleiermacher rightly op- 
poses ;—an essential part in the formation of notions is attributed 
to organic function. This part is to be more closely defined 
by this, that by it the external orderly arrangement in space 
and time is brought to consciousness. Then thinking led 
from the signs contained in it to the internal orderly arrange- 
ment, makes it signify the moments constituting the essence of 
things. This is also the way in which the individual sciences 
actually proceed in the construction of their notions and judg- 
ments. The system of notions is not given in a lasting way 
in the general subjective reason. It exists in the absolute 
reason which comprehends all mere subjectivity and adjusts 
it to objectivity. It is therefore as essentially requisite for 
the subject, in order to reach science, to advance by means 
of organic function, which is more powerful in relation to 
objectivity, as to verify its results by means of its own in- 
tellectual power, which works more independently in the service 
of the end and aim of knowledge. 

This also presupposes that organic function is not a ‘ chaotic 
manifold of impressions,’ but is orderly, the mirroring of the 
orderly arrangement in space and time which belongs to things, 
and can warrant a sure starting-point for thought. Schleier- 
macher himself almost expressly recognises this, when he 
makes the correspondence between thought and (external) 
existence to be brought about by the real relation in which the 
totality of existence stands to the organism ;' for this presupposes 
that this higher significance belongs to organic function. The 
ascription of a chaotic character to organic function can only 
be viewed as a remaining part of the Kantian subjectivism not 


1 Dial. § 106. 




















108 § 44. Reality of Space and Time. 





yet overcome, which supposes that all orderly arrangement 
originates in the spontaneity of the subject, and must con- 
sequently be quite different from organic affection. The op- 
posite expressions of Schleiermacher, on the other hand, rest 
on the deeper and truer thought of a conformability to law 
dwelling in the external reality, according to which organic 
affection, as the immediate action of things in us, or as ‘ our 
existence in so far as it is identical with the existence established 
without us,’ must bear the character of an arrangement con- 
formable to.reason.? 

[The reality of Space and Time appears to be a necessary 
element in the Hamiltonian Philosophy of Common Sense, but 
we do not find Sir Wm. Hamilton giving thoroughly consistent 
utterances on this subject. He sometimes unreservedly assents 
to the Kantian doctrine; at others he insists upon adding to 
the a priori and subjective Space and Time of Kant an a 
posteriori and objective Space and Time acquired in percep- 
tion ;? while his doctrine of the primary qualities of matter 


1 Dial. p. 56. 

2 In connection with this whole paragraph, ef. the Author’s tract, 
Zur logischen Theorie der Wahrnehmung und der zunächst an die 
Wahrnehmung geknüpften Erkenntnissweisen, in Fichte’s Zeitschrift 
für Phil, New Series (Halle, 1857), xxx. 191-225 (especially 
pp. 222-24, on the Reality of Space) ;—also my tract, Zur Theorie der 
Richtung des Sehens, in Henle’s and Pfeuffer’s Zeitschr. für rationelle 
Medicin, 3rd Series, 1858, v. 268-82 (especially on the distinction of 
the objectively-real space from the space of the field of vision). Cf. also 
my notes to my translation of Berkeley’s Principles of Human Know- 
ledge, Berlin, 1869. 

The argument stated above for the extension of ‘ things-in-themselves’ 
in three dimensions, has been combated by Alb. Lange in his Ge- 
schichte des Materialismus, pp. 497-99, Iserlohn, 1866. I have answered 
it partly in my Grundr. der Geschichte der Philos. 1st ed. iii. 279, 
Berlin, 1866 ; p. 303, 2nd ed. 1868; and partly in this edition of my 
Logik, in the notes appended to this section. Cf. my tract Der Grund- 
gedanke des Kantischen Kriticismus nach seiner Entstehungszeit und 
seinem wissenschaftlichen Werth in the Altpreuss. Monatschrift, 1869, 
vi. pp. 215-24. 

3 [Cf. Hamilton’s edition of Reid’s Works, p. 126, note; Reid's 


§ 44. Realty of Space and Time. 109 





implies that space is known a priori and as objective. As the 
doctrine of the primary qualities is most essential to his system 
of philosophy, and most carefully elaborated by Hamilton, we 
may take it as his final deliverance. The primary qualities 
are all derivable from Space. They are, in fact, forms of 
Space. They are known as objective, and they are known a 
priori. Hence Hamilton must be held to believe in the ob- 
jective existence and & priori nature of Space. He has not so 
explicitly expressed his opinion with regard to Time.’ 

Mr. Mill and his School deny the objective reality of Space 
and of Time. They are sensations worked up into permanent 
possibilities of sensation. All that they possess of reality, 1.6. 
permanence, and objectivity, i.e. power to affect not one per- 
ceiving subject but several at the same time, they owe to the 
laws of association.? Berkeley and Prof. Fraser, while they 
refuse to believe in any other Space and Time than Sensible 
Space and Sensible Time, recognise: (1) An externality to 
our present and transient experience in our own possible ex- 
perience past and future, and (2) An externality to our own 
conscious experience, in the contemporaneous, as well as in 
the past or future experience of other minds; and therefore 
admit the reality of space and time as far as that is contended 
for in this section.?] 


Works, p. 841; Discussions, p. 273 ; Lect. on Metaph. i. 403; ii. 114, 
166-70. 

1 Cf. for a very severe criticism of Hamilton’s theory, Dr. J. H. 
Stirling’s Philosophy of Perception, pp. 69-87 and passim. 

2 Cf J. S. Mill’s Examination of Sir Wm. Hamilton's Philosophy, 
8rd ed. pp. 258-304; Bain’s Senses and Intellect, 2nd ed. pp. 111, 
197, 250, 370, 637. Cf. for an analogous doctrine, Herbert Spencer, 
Psychology, pp. 52, 244, 309. 

3 Cf. the Life and Letters, &c. of Bishop Berkeley, by Prof. Fraser, 
Oxford, Clarendon Press, 1871, ch. x. ] 























110 ὃ 45. /ndividual Conception of Intuition. 





PART SECOND. 


THE INDIVIDUAL CONCEPTION OR INTUITION IN ITS 
RELATION TO THE OBJECTIVE INDIVIDUAL EX- 
ISTENCE. 


$ 45. THE rvDIVIDUAL CONCEPTION Or INTUITION 
(representatio or conceptus singularis) is the mental 
picture of the individual existence, which is (or at least 
is supposed to be) objective. 


External orderly arrangement, or that in Space and Time, 
which is represented by perception, is to be explained by the 
thought of the internal orderly arrangement, in which it is 
reflected. The first step towards the solution of the problem 
is naturally the discrimination of individuals by means of indi- 
vidual conceptions. 

The word conception is not used here to mean a perception 
reproduced, nor to mean a mental product generally. It means 
the mental picture of an individual existence, whether presented 
in perception or reproduced in memory. A conception may be 
either an individual conception or intuition, which has to do 
with one individual (or with what belongs to one individual), 
or a general conception, which refers to a mutually-related 
group of individuals (or of what belongs to individuals), and 
forms the approximate mental (psychic) basis for the notion. 


In this section we shall explain what belongs equally to both 
kinds of conception. 


§ 46. The Distinction of Individuals, etc. 111 





§ 46. Individual intuitions gradually arise out of the 
original blur of perception, when man first begins to 
recognise himself, an zndividual essence in opposition to 
the outer world. This form of individual existence or 
individuality is transferred to any external existence 
whose appearance betokens that it can be isolated or set 
over against other phenomena. The logical correctness 
of the application of this form of knowledge is to be 
tested by the same criteria as the truth (cf. § 42) of all 
those elements of knowledge which originate in our 
internal, and go to complete our sense-perception. For: 
(a) (cf. § 40) In reference to one’s own person, self- 
consciousness directly warrants the reality of our in- 
dividual existence. (b) (cf. § 41) An existence analo- 
gous to our own must be attributed to all other 
persons, and therefore the form of existence as an 
individual essence. (c) (cf. § 42) The analogy of 
things without us to our own essence decreases 
gradually, but never vanishes wholly at any point. 
Hence we may allow ourselves to believe that the parti- 
tion of the totality of impersonal existence into rela- 
tively independent individuals actually takes place, and 
is not brought by us by means of a merely subjective 
necessity. The sense-phenomena, however, taken along 
with the analogous gradations in the department of 
mental life, prove that the boundary, the individual de- 
terminate existence, and its development into a greater 
whole, becomes more indistinct and indefinite the lower. 
any object stands on the gradual series of essences. 
(d) On the other side, the most complete individual 
independence, together with the widest and most inti- 














112 § 46. The Distinction of Individuals 





mate community of life and action, is to be found along 
with the greatest mental and moral height in the scale 
of being. 

The intuition, or the individual conception, like per- 
ception ($$ 41-42), is correctly formed in proportion as 
the gradations in question have been observed. 


The problems here treated often come up in the positive 
seiences of Botany and Zoology in particular cases. Their 
full solution cannot be reached by the special means which 
these sciences have at their disposal, but only by reference to 
general considerations belonging to Logic or the theory of 
knowledge. Aristotle does not enter very deeply into these 
questions either in his physical or in his metaphysical and logical 
writings. He calls individual essences the first substances 
(πρῶται οὐσίαι), without submitting to a stricter investigation 
the knowableness, essence, and limits of individuality. Ques- 
tions such as the following first arose in modern times, and 
received full attention as scientific problems:—Is the true indi- 
vidual the plant or the single shoot (eye, bud, &c.; “ gemmae 
totidem herbae,’ Linnaeus; cf. Roeper, Linnaea, p. 434, and 
other later botanical writings), the coral stem or the single 
coral insect? How far is the life of the embryo individual 
and independent, and how far part of the life of the mother, 
&c.? In natural science it has been seen that the individual 
cannot pretend to more reality than belongs to the genus, 
species and individual; that the individual is characterised 
not by unity of sensible appearance, but by unity in the 
course of development ; that the individual plant is far inferior 
to the individual animal in internal unity. Cf. Rud. Virchow, 
Atome und Individuen, a lecture delivered in 1859,' where 
the individual is defined to be ‘a single community where all 
| parts co-operate to a similar end or act according to a definite 


plan.’ 


! Published in Vier Reden über Leben und Kranksein, pp. 35-76, 
Berlin, 1862. 


by means of Individual Conceptions. 113 





In other provinces also the consciousness of the gradations 
of individuality is an essentially scientific demand, and a con- 
dition without which a solution of many important questions of 
debate cannot be reached. For example, the Homeric ques- 
tion between unitarians and separatists can only be got rid 
of by the scientific view (already attained by Aristotle) that 
the epic poem, because of its nature as an earlier and lower 
stage in the development of poetry, does not possess the strict 
comprehensive unity of the Drama, and yet does not exclude a 
certain poetic unity. The individual epic poet of that early 
age, belonging to an associated company of minstrels, had less 
independent individuality within his circle than the dramatist. 
The question to be asked is not, therefore, whether the poem is 
to be ascribed to one or to many, but what part of it is to be 
ascribed to the one and what to the many ?--or, more particu- 
larly, what is to be presupposed as the pre-Homeric foundation? 
what is to be considered as the work of one master, who, trained 
in intimacy with the smaller poems of the earlier minstrels 
who sung the history and tales of the people, seized on and 
realised the thought of the greater epic? and what has been 
added by post-Homeric poets, and what praise or blame 
belongs to the rhapsodists, to the collectors, and, lastly, to the 
grammarians who arranged and made emendations and explan- 
ations ? 

The doctrine of Spinoza reduces all individuality to the same 
dead level of meaninglessness. The Letbnizian and Herbartian 
doctrine of monads, with equal incorrectness, transfers that 
full comprehensive individuality which belongs to the personal 
human spirit to the lowest bases of organic and inorganic life 
which they believe to be independent individual essences with- 
out extension in space. The Kantian critical philosophy believes 
that it has found the true mean between these two extremes, 
in the doctrine of the impossibility of settling the problem in 
question theoretically. It enumerates among the subjective 
elements of knowledge the categories of Unity, Plurality, and 
Totality, which, founded on the organisation of our means of 
knowing, are necessarily transferred by us to the world of 


I 





peace ee ας. eh et = ----- 


— mn 


u ne ππ πὸ 


114 ὃ 47. Individual Conception and Existence. 





phenomena, but find no application to real existences or to 
things-in-themselves. Schelling, Hegel, and Schleiermacher, on 
the other hand, believe that these forms have a real validity. 
But when they come to determine the different gradations of 
individuality, Schelling and Hegel approach very closely the 
doctrine of Unity founded by Spinoza, and Schleiermacher, in 
certain considerations, almost adopts the individualism of Leib- 
niz and Herbart. 

[In Mr. Mill’s system of philosophy, where all independent 
and objective reality depends only on association, where all 
external and internal things are only congeries of possibilities 
of sensation, there seems no place for a theory of individuality. 
But the fact that, so far as regards mind, there always remains 
a final inexplicability unable to be resolved into a series of 
feelings affords a basis for our own existence as an individual. 
And Mr. Mill’s theory of inseparable association, i.e. that when 
certain sensations have been thought of together in certain 
ways they cannot be thought as existing apart, combined with 
his theory of the chemical composition of causes, according to 
which a whole of association may have a character which is quite 
different from the sum of the characters of the associated parts, 
affords ground for the individual existence of things."] 


§ 47. As the individual conception corresponds gene- 
rally to the individual existence, so is different kinds 
or forms correspond to the different kinds or forms of 
individual existence. The individual existence is first 
recognised in independent objects. When the object of a 
conception makes up a whole, in which different parts, 
attributes, and relations may be distinguished, the dif- 
ferent elements of such a conception may be considered 
singly to be conceptions. We must distinguish two 
cases here. Either the form of objective independence 


(? Cf. Exam. of Sir Wm. Hamilton's Philos. pp. 234-43, 305-27; 
and Logic, 7th ed. 405-12.] 





The Categories in the Aristotelian Sense, etc. 115 





is attributed to the objects of these conceptions, with 
the consciousness that this independence is only ima- 
gined not real, or these objects are absolutely perceived 
to be not independent. On these relations are based 
the forms of the substantially concrete, the substantially 
abstract, and the verbal, attributive, and relative concep- 
tion. The forms of the individual conceptions and of 
their verbal expression, in their relation to the corre- 
sponding forms of existence (and these last themselves 
metaphorically), are the Categories in the Aristotelian 
sense of the word. . 


All these Categories are transferred from objectively 
valid conceptions to those whose objects are mere 
fictions (e.g. to mythical beings). 


As the (logical) forms of conception correspond to the 
(metaphysical) forms of individual existence, so the (gram- 
matical) forms or parts of speech correspond to the logical. A 
word is the expression in speech of a conception. The conception 
of an independently existing object is expressed by the concrete 
substantive, to which must be added the substantive pronoun, 
which denotes a person or thing in its relation to the speaker. 
The conception of that which does not exist independently, 
but is intuitively perceived under the borrowed form of 
individual existence, is denoted by the abstract substantive. 
The conception of that which does not exist independently, as 
such, whether an act, property (or quality), or relation, is 
expressed by the verb, the adjective with the adjective pronoun, 
and the adverb, and by the preposition with the forms of 
inflection. Numerals can only be understood on the basis of 
the formation of notions; for they presuppose the subsumption 
of similar objects under the same notion. Conjunctions can 
only be comprehended on the basis of the formation of judg- 
ments and inferences; for they bind together sentences and 
parts of sentences, whose opposite references express the corre- 


53 





% 
rap nn a en EAE oe Be en 
N baby ‘ 
Ben nur A Se 2. 

















Pe bs es ++ eee ee et a --- τ΄ 





116 ὃ 47. Individual Conception and Existence. 





sponding relations of conceptions to each other, which on their 
side again must rest on relations between real combinations. 
(Prepositions, on the other hand, by means of the relations 
between single words and complexes of words, which express 
the corresponding relations between single conceptions, denote 
the relations of single things, actions, &c. to each other.) 
Interjections are not properly words, but only direct expres- 
sion of feelings not developed into conceptions or thoughts. 
‘The construction of all language proves that the oldest 
form was essentially that which is preserved in some lan- 
guages of the simplest construction (e.g. in the Chinese). 
All languages have started from significant sounds, simple 
sounds picturing intuitions, conceptions, and notions, which 
do duty in every relation, 1.6. as every grammatical form, 
without requiring for each function an audible expression— 
so to speak, an organ. In this earliest stage in the growth 
of languages neither verbs nor nouns, conjugation nor de- 
clension, are to be distinctively distinguished. The oldest 
form for the words which now sound deed, done, do, doer, 
doing, was, when the Indo-Germanic stem-language arose, 
dha; for this dha (i.e. to set, to do—Old Indian dha, Old 
Bactrian dha, Greek 92, Lithuanian and Slavonic de, Gothic 
da, High German ta) appears to be the common root of all 
these words. In a somewhat later stage of the develop- 
ment of the Indo-Germanic language, in order to express 
distinct references, they repeated the roots twice, not yet 
supposed to be words, along with another root, and linked 
them together into a word. In order, for example, to de- 
ncte the first person of the present, they said dha-dha-mi, 
from which, in the later stage of the growth of the language, 
by fusion of the elements into one whole, and by the con- 
sequent possibility of change, came the root dhadhami (Old 
Indian dädhämi, Old Bactrian dadhämi, Greek τίθημι, Old 
High German töm, tuom; tétami, New High German thue). 
In that earliest form dha there lay, as yet unseparated and 
undeveloped, the different grammatical references, their whole 
verbal and nominal modifications ; and this can still be observed 


The Categories in the Aristotelian Sense, etc. 117 








in languages which have remained in the stage of simplest 
development. This example, selected by accident, represents 
all the words of the Indo-Germanic language.’! 

The logical consciousness of the different forms of concep- 
tion originally developed itself with and in the grammatical 
consciousness of the different parts of speech, and with the meta- 
physical consciousness of the different forms of existence.? 

Plato recognises the grammatical opposition of the ὄνομα 
and ῥῆμα The author of the dialogue Sophistes‘ refers 
them to the opposition between the corresponding forms of 
existence—Thing and Action—and refers these last to the 
more general opposition of Rest and Motion, which he imme- 
diately subserves together with that of Identity and Difference 
under the universal unity of Being. Ä 

Aristotle developes the division of the parts of speech by 
adding the σύνδεσμος or Particle (the more special meaning 
of conjunction was first given to this word by later gramma- 
rians). He taught that the word, the ὄνομα and the ῥῆμα, cor- 
responds to the conception, the νόημα :---ἔστι μὲν οὖν τὰ ἐν 
τῇ φωνῇ τῶν ἐν τῇ ψυχῇ παθημάτων σύμβολα.---τὰ οὖν ὀνόματα 
αὐτὰ καὶ τὰ ῥήματα ἔοικε τῷ ἄνευ avi θέσεως καὶ διαιρέσεως νοή- 
ματι (De Interpr. 1). The ὄνομα is a conventional designation 
which does not include a reference to time, but the ῥῆμα does. 
The σύνδεσμος, according to Aristotle, is a dependent φωνὴ 
ἄσημος, e.g. μέν, ἤτοι, δή. In the Poétics (ec. xx.) the ἄρθρον is 
also named; but the reading is uncertain, and the genuineness 
of the passage doubtful. Aristotle calls single conceptions and 
words τὰ ἄνευ συμπλοκῆς, τὰ κατὰ μηδεμίαν συμπλοκὴν λεγό- 

! Aug. Schleicher, Die Darwin’sche Theorie und die Sprachwissen- 
schaft, pp. 21-23, Weimar, 1863. 

? Cf. Classen, De Gramm. Graecae Primordiis, Bonn, 1829; L, Lersch, 
Die Sprachphilosophie der Alten, Bonn, 1838-41 ; Bd. ii. (die Sprach- 
kategorien), Bonn, 1840; G. F. Schömann, Die Lehre von den Rede- 


theilen nach den Alten, Berlin, 1862; H. Steinthal, Geschichte der 
Sprachwiss. bei den Griechen und Römern (with special reference to 
Logic), Berlin, 1863. 

° Theaet. p. 206 D; cf. Cratylus, p. 399 B. 4 P. 261 Ε sqq. 

° De Interp. c. ii. ff.; Poét. c. xx. (cf. notes to my ed. and transl.). 











ren ag ae . ΡῈ - 
= nn EEE ET ET LED EU 
u vi 4: En . 


mg 





ea ee τις τ" ie re 


-- -- ----Ξ- --- 











118 ὃ 47. Individual Conception and Existence. 





peva,' i.e. the uncombined elements, into which the proposition 
or judgment (λόγος) dissolves when analysed. Aristotle 
divides conceptions according to their formal points of differ- 
ence. In this division he proceeds on the fundamental 
thought that conceptions as elements of thought must corre- 
spond with the elements of what actually exists objectively, 
and their differences of form to the differences of form in what 
is conceived. Every conception, and so also its verbal expres- 
sion or word, must denote either: 1. a substance; 2. a quan- 
tity; 3. aquality; 4. arelation; 5. a where; 6. a when; 
7. a position; 8. a habit; 9. an action; or 10. a passion : — 
Τῶν κατὰ μηδεμίαν συμπλοκὴν λεγομένων ἕκαστον ἤτοι οὐσίαν 
σημαίνει ἢ ποσὸν ἢ ποιὸν ἢ πρός τι ἢ ποὺ ἢ ποτὲ ἢ κεῖσθαι 
ἢ ἔχειν ἢ ποιεῖν ἢ πάσχειν (De Categ. iv. 1 B, 28. The 
Aristotelian examples are: 1. ἄνθρωπος. ἵππος; 2. δίπηχυ; 
τρίπηχυ; 3. λευκόν, γραμματικόν ; 4. διπλάσιον, ἥμισυ, μεῖζον ; 
5. ἐν Λυκείῳ, ἐν ἀγορᾷ ; 6. ἐχθές, πέρυσιν ; 7. ἀνάκειται, κάθηται : 
8. ἀναδέδεται, ὥπλισται ; 9. τέμνει, καίει; 10. τέμνεται; καίεται. 
The Categories are stated in this completeness in the 
Topics,? where the first, as commonly happens, is called τί 
ἐστιν. Single categories are mentioned in many places. 
Anal. Post. i. 22, Phys. v. 1, Metaphys. v. 7, leave out 
κεῖσθαι and ἔχειν. In Anal. Post. i. 22, οὐσία is opposed to 
συμβεβηκότα. Aristotle calls these ten forms τὰ γένη or τὰ 
σχήματα τῆς κατηγορίας or τῶν κατηγοριῶν. The shorter and 
more convenient designation, κατηγορίαι, occurs repeatedly. 
With Aristotle κατηγορία means originally assertion or predic- 
ation, and so the expression τὰ γένη τῶν κατηγοριῶν OY al κατη- 
yopiat may be translated the kinds of assertions or of predicates. 
If, then, Category means that which naturally takes the place 
of predicate, this meaning would suit most of the last nine 
forms, but would not suit the first, for the first naturally takes 
the place of the subject. It is only the conceptions of genera 
or of the so-called second substances of Aristotle, not the indi- 


1 Cat. c. ii. 1 a, 16; ὁ iv. 1 B, 25. 2 1. 9, 103 2, 20. 
3 Prantl (Gesch. der Logik) gives a very good tabular scheme of the 
places where they are mentioned. 


The Categories in the Aristotelian Sense, etc. 119 





vidual conception which belongs to the individual substance, to 
substance in the first and fullest sense of the word, that take 
easily and naturally the place of the predicate. The individual 
substance, on the other hand, can only be asserted as predicate 
in combination with a subject not determined according to its 
proper nature; as, e.g. in the sentences—‘ This wise man is 
Socrates,’ “ This one who approaches is Callias.’ 

But since Aristotle has also included individual substances 
under the designation κατηγορίαι, he cannot mean predicates 
in general, but predicates of certain propositions. The full 
designation κατηγορίαι τοῦ ὄντος, or τῶν ὄντων, shows what pro- 
positions Aristotle has in view. Every ὄν (in the widest sense 
of the word) is either an οὐσία or a ποσόν or a ποιόν, &e. 
All definite conceptions, whether substantive, adjective or 
verbal, &c., are predicates of their objects, the things, pro- 
perties, actions, &c. in a proposition whose subject is formed 
of this object conceived only indistinctly as any kind of ὄντα 
in general. Τοῦτο τὸ dv, or τὸ Tporeiusvov,! or τὸ ἐκκείμενον,3 
is to be thought of as subject. By a well-known and 
not uncommon grammatical analogy the plural denotes the 
kinds; the κατηγορίαι τοῦ övros? are the kinds or different 
forms of categories, i.e. of predications, and also conceptions, 
of the existent so far as they correspond to the kinds or differ- 
ent forms of the existent, and by metonomy are these last 
themselves. The notion, kinds or forms, may be expressed 
not only by the plural, but also by a word added to κατηγορία 
or κατηγορίαι, such as σχήματα or γένη. Τὸ σχῆμα τῆς κατη- 
γορίας is the kind of assertion about the existent, of predica- 
tion of the existent, or form of conceiving the existent, whether 
the conception be substantive, i.e. denoting what is substantial, 
or adjective, i.e. denoting a quality, &c.* The first Category, 
that of substance, belongs, according to Aristotle, partly to his 
so-called first substances (πρῶται οὐσίαι), i.e. individuals, partly 
to second substances (δεύτεραι οὐσίαι), i.e. kinds and genera. 
In the first substances Aristotle distinguishes matter (ὕλη or 


' According to Top. i. 5, p. 102 a, 34. ? Ibid. i. 9, p. 103, B, 30. 
3 Metaph. ix. 1, 1045 B, 28. 4 Ibid. v. 28, § 7. 























120 § 47. [Individual Conception and Existence. 





ὑποκείμενον), form (εἶδος or μορφή or τὸ τί ἢν εἶναι, Or ἡ κατὰ 
λόγον οὐσία), and the whole (τὸ ἐκ τούτων ἀμφοῖν OY τὸ σύνολον). 
Aristotle comprehends! the nine remaining kinds of concep- 
tion under the common name of τὰ συμβεβηκότα. He some- 


times distinguishes? three chief classes, οὐσία, πάθη, and πρός 


τι.3 - 


I Analyt. Post. i. 22, 83 A, 25. 

2 Metaph. xiv. 2, 1089 B, 23. 

3 It is not certain how this doctrine of the Categories may have 
developed itself in the mind of Aristotle. Trendelenburg* believes that 
Aristotle had been led to it by the consideration of grammatical rela- 
tions—viz. of the parts of speech—whose characteristics were embodied 
in the terms (πτώσεις). The relationship of the doctrine of the Cate- 
gories to the grammatical doctrine of the parts of speech has been 
thoroughly, acutely, and evidently exhibited by Trendelenburg. But 
it is at least doubtful that the origin of the doctrine of the Categories 
was a consideration of the parts of speech and their distinction according 
to πτώσεις. The Aristotelian division of the parts of speech (see above) 
is too little developed to favour this assertion. ὄνομα and ῥῆμα corre- 
spond well enough to οὐσία and συμβεβηκός, but cannot supply a basis 
for the ten categories. Moreover, Aristotle adds to the πτώσεις ft forms 
of verbal inflection on which he has based no verbal categories (as the 
tenses byiavey and ὑγιανεῖ). When he further acduces a substantive 
(καιρός) as an example of a logical πρός τι, this is evidently independent 
of the distinction of the parts of speech, and rests on essentially dif- 
ferent grounds. 

Aristotle, as Trendelenburg himself recognises, has distinguished not 
so much parts of speech as parts of the sentence (subject and predicate, 
and different forms of the predicate). He defines: ὄνομά ἐστι φωνὴ 
σημαντικὴ κατὰ συνδήκην ἄνευ χρόνου ---ῥῆμα δέ ἐστι τὸ προσσημαῖνον 
xpövov;f but adjectives (such as δίκαιος, λευκός), as far as they are 
predicates with ἐστίν, are considered to be ῥῆματα ;§ although elsewhere 
λευκὸς is called ὄνομα, because it does not connote time. In the dis- 
tinction of ὀνόματα and ῥήματα, and in the distinction of ra κατὰ μηδε- 
μίαν συμπλοκὴν λεγόμενα, Aristotle seems to have kept to the empirically 
given forms of sentences, such‘as ‘ Socrates is wise, Socrates disputes, is 





* De Arist. Categ. 1833; Geschichte der Kategorienlehre, pp. 11-13, 
1845. 
t De Interp. c. iii. 168, 16. f Ibid. c. 1. and ii. § Ibid. ς. 1. and x. 


The Categories in the Aristotelian Sense, etc. 121 





The Stoics reduced the ten Aristotelian Categories to four, 
which they call τὰ γενικώτατα (the most universal kinds), and 


refuted,’ &c. The distinction of ὀνόματα and ῥήματα seems to have 
been the basis of that of οὐσίαι and πάθη, and the distinction of the parts 
of speech seems to have been the basis of that of the nine kinds of 
συμβεβηκότα. 

Still Aristotle in his construction of the doctrine of the Categories 
may have been influenced by definite philosophical references, and 
especially by his polemic against the Platonic doctrine of ideas. Aris- 
totle sought to recognise the universal in the particular. He based his 
speculation on the empirical, and tested the truth of the doctrine of 


~ ideas in its relation to the actual existence presented to him. In this 


critical endeavour it could not have escaped his quick glance that all 
phenomena are not to be considered in the same way as pictures of ideas. 
Some contradicted this view in formal reference. When he came to 
account for this inconsistency, he must have found its cause in this, that 
Plato thought his ideas, and could only think them as ideas, under a 
single form of existence, the form of substantiality ; while what actu- 
ally exists is represented under different forms. The idea of the good, e.g. 
must be of substantial existence, and at the same time must be the common 
ideal for everything which actually appears good. But this latter is only 
in part something substantial, as God, the νοῦς (thought substantial by 
Aristotle). Itis partly something praedicative or accidental—an action, 
a property, a relation ; as, a good deed, the goods of the mind, the use- 
fulness of means to an end, &c. This formal difference contradicts the 
formal unity of the common ideal accepted by Plato.* The methodical 
and systematising mind of Aristotle, led to pay attention to the 
difference of the forms of existence by considerations of this kind, would 
soon attempt to draw up a comprehensive series of these. In his investi- 
gation into the Categories, he had positive points of connection with 
the investigations, carried on by Plato or a Platonist in the Sophistes, 
upon the Existent generally, about thing and action, resistance and 
motion, identity and difference, unity, indefinite greatness and smallness, 
and in the further discussionsf upon relative notions, upon ποιεῖν and 
πάσχειν, as kinds of γένεσις. But these would assist him only in a small 
degree, because with Plato the question of the forms of the individual 
existence is entirely subordinated to the question of the relation of the 





* Arist. Eth. Nic. i.4; Eth. Eud.i. 8; Metaph. i. 9, xiii. 4, xiv. 2. 
+ As in De Rep. iv. 438. t Soph. p. 248. 


























122 § 47. /ndividual Conception and Existence. 








believe to be forms of objective reality. They are—1. The Sub- 
strate (τὸ ὑποκείμενον); 2. The (essential) Property (τὸ ποιόν) ; 
3. The (unessential) Quality (τὸ πὼς ἔχον); 4. The Relation 
(τὸ πρός τι πὼς ἔχον). They subordinate all these Categories 
to the most universal of all notions, to that of ὄν or (probably 
later) to that of ri. The Stoics also develope the doctrine of 
the parts of speech. They define the ἄρθρον as a species 
of word, the article namely, and they afterwards add the 
adverb (πανδέκτης or ἐπίῤῥημα), and divide the ὄνομα into 
κύριον and προσηγορία" The ἐπίῤῥημα serves for the extension 
of the predicate, and the σύνδεσμος for the combination of the 
chief parts of discourse with each other. The doctrine of the 
eight parts of speech first arose in the Alexandrine era. The 
constituent parts of the thought, and therefore of speech, had 
been separated by philosophers from the logical point of view. 
The grammarians undertook to arrange the empirically given 
material of language. They joined to single definite parts of 
speech the terms used by philosophers in a wider sense, and 
they introduced new terms for the others. The σύνδεσμος, which 


individual to the universal. The elaboration of the Categories is rather 
to be considered as the independent work of Aristotle. 

Cf. Bonitz, Sitzungsberichte der phil.-hist. Classe der Wiener Akad. 
der Wiss. Bd. x. pp. 591-645, 1853; Brandis, Gesch. der Gr.-Röm. 
Phil. ü. 2 A, p. 375 ff.; Prantl, Gesch. der Logik, i. p. 182 ff., 1855; 
Wilh. Schuppe, Die Aristotelischen Kategorien, im Jubiläumsprogramm 
des Gleiwitzer Gymnasiums, Gleiwitz, 1866. [Cf. also Mansel, in his 
edition of Aldrich, Appendix, Note B, p. 175, where he follows 
Trendelenburg. ] 

! These categories correspond to the three classes of categories placed 
together by Aristotle (Metaph. xiv. 2, 1089 B, 23)—ra μὲν yap οὐσίαι, 
ra δὲ πάθη, ra δὲ πρός rı—the first and second to the first, the third to 
the second, and the fourth to the third. 

2 Diog. Laert. vii. 57; Charis. ii. 175. Cf. Priscian, ii. 15, 16: 
Partes igitur orationis secundum dialecticos duae, nomen et verbum ; 
quia hae solae etiam per se conjunctae plenam faciunt orationem ; alias 
autem partes syncategoremata, hoc est consignificantia appellabant : 
secundum Stoicos vero quinque sunt ejus partes—nomen, appellatio, 
verbum, pronomen sive articulus, conjunctio. 


The Categories in the Aristotelian Sense, etc. 123 





had denoted both conjunction and preposition, from this time 
denoted the former only, and the preposition’ was called the 
πρόθεσις. The ἀντωνυμία (the pronoun) was separated from 
the noun. The participle (μετοχή) came in between the verb 
and the noun. Adjectives and numerals were added to 
the noun. The interjection was not reckoned an actual 
part of speech. Priscian, in his enumeration of the ‘ octo 
partes orationis,’ followed in the footsteps of Apollonius Dys- 
colus. His theory remained the standard one for following 
times, while the Aristotelian doctrine of the Categories pre- 
vailed in the Middle Ages. 

The formal metaphysical notions of Des Cartes and Spinoza 
—substantia, attributum, modus; those of Zocke—substance, 
mode, relation; those of Wolff—ens, essentialia, attributa, 
moili, relationes extrinsecae—are related to the Stoical doctrine 
of the Categories. The Leibnizian five universal divisions of 
essence (cinq titres généraux des étres)—Substances, Quan- 
tities, Qualities, Action or Passion, and Relations—come 
nearer the Aristotelian division. 

The Kantian Categories, or ‘ pure stem-notions of the under- 
standing,’ do not serve as the metaphysical basis of forms of 
conception, but of relations of judgments. 

Herbart considers the forms of common experience—Thing, 
Property, Relation, Negation; and the categories of the 
internal apperception—Sensation, Science, Volition, Action— 
to be the results of the psychological mechanism, and without 
metaphysical or logical significance. 

Hegel understands by the Categories, the universal, intelli- 
gible essentialities which enmesh all actuality. 

Schleiermacher founds his formal division of notions into 
‘subject and predicate notions,’ which he makes parallel with 
the grammatical division of words denoting notions into nouns 
and verbs, on the distinction of the forms of existence, of 
being set for itself, and of co-existence, or of things and actions. 
Abstract nouns are substantives which make the action sub- 


1 Perhaps Aristotle’s ἄρθρον is the preposition and also the article ; 
cf. my transl. of the Poetics, Berl. 1869, note 99. 























$47. Individual Conception and Existence, etc. 





stantive in order to use it as a subject. Co-existence divides 
into activity and passivity, doing and suffering. The ad- 
jective which expresses the quality—i.e. the result of an 
activity already embodied in substantial existence, must be 
thought to arise by means of participles and other verbals out 
of the verbs (Dial. p. 197). 

Lotze' divides the manifold notions we find in our consci- 
ousness into three great groups of object-notions, predicative 
(i.e. verbal and adjectival) notions, and relation-notions. In 
each the peculiarity of the central point, as the point of dis- 
tribution of the attributes, conditions the whole configuration 
of the parts. 

| Hamilton thinks that the doctrine of the Categories belongs 
to Metaphysics, not to Logic. He regards the Categories of 
Aristotle as a classification of existences, and thinks them 
liable as such to many objections. He would substitute for 
them: 1. The Supreme Category Being (τὸ ὄν, ens). This is 
primarily divided into, 2. Being by itself (ens per se), and 
3. Being by accident. Being by itself is the first Category 
of Aristotle. Being by accident includes his other nine.? 

J. S. Mill thinks the Categories of Aristotle an enumera- 
tion of nameable things, and as such ‘a mere catalogue of the 
distinctions rudely marked out by the language of familiar 
life, with little or no attempt to penetrate, by philosophical 
analysis, to the rationale even of those common distinctions.’ 
As ‘a substitute for this abortive classification of existences ’ 
Mr. Mill offers the following:—1. Feelings, or States of con- 
sciousness. 2. The Minds which experience these feelings. 
3. The Bodies, or external objects, which excite certain of 
those feelings, together with the powers or properties whereby 
they excite them. 4. The Successions and Co-existences, 
the Likenesses and Unlikenesses, between feelings or states 
of consciousness.?] 

Cf. Trendelenburg, Gesch. der Kategorienlehre, Berl. 1846. 


I Log. p. 77; cf. pp. 42, 50. 2 [ Lect. on Metaph. i. 197-201. 
3 Logic, 7th ed. i. 49-84. ] 


SS 48, 49..Clearness and Distinctness. Attributes. 125 


4 

§ 48. A conception is clear (notio clara in opposition 
to notio obscura) when it has sufficient strength of 
consciousness to enable us to distinguish its object 
from all other objects. It is distinct (notio distincta 
in opposition to notio ccnfusa) when its individual 
elements are also clear, and consequently when it 
suffices to distinguish the elements of its object from 
each other. 


The Cartesian criterion of truth (s. § 24) gave rise to a 
closer enquiry into the essential nature of clearness and dis- 
tinctness. The definitions given above are those of Leibniz 
(§ 27). They are to be found in all the Logics of the 
Wolffian and Kantian period, where a fundamental signi- 
ficance is often attached to them. Some of the later logi- 
cians, on the other hand, have undeservedly disregarded them. 
Clearness and distinctness were overrated in the seventeenth 
and eighteenth centuries, but were undervalued in the first 
half of the nineteenth. 


§ 49. An Attribute (nota, τεκμήριον) of an object is 
everything in it, by which it is distinguished from other 
objects. The conception of an attribute is contained in 
the conception of the object as a part of its conception 
(representatio particularis). 


Attributes are attributes of things, of an object which is real 
(or conceived as if it were real). One can only speak cor- 
rectly of the attributes of a conception in so far as it is con- 
sidered to be something objective, i.e. as it is the object of 
thinking directed upon it. ‘To receive an attribute into a 
conception’ is a shorter expression for ‘to bring into con- 
sciousness the attribute of a thing by means of the correspond- 
ing part-conception, or to receive into the conception an 
element by means of which the attribute of the thing under 
consideration is conceived. 




















— - = 
en re 
ne Te in Ge tt Seen 


126 ὃ 50. Content of a Conception. Its Partition. 





§ 50. The individual attributes of an object do not 


make a mere aggregate, but stand to each other and to 
the whole in definite relations, on which depend their 
grouping together, their peculiar character, and their 
very existence. This real relation must mirror itself 
in the relation of the part-conceptions to each other and 
to the whole conception. The sum total of the part- 
conceptions is the content (complexus) of a conception. 
The analysis of the content of a conception into part- 
conceptions, or the statement of the individual attri- 
butes of its object, is called partition. 


So far as the subjectively-formal Logic leaves unnoticed 
that real relation, it can only apprehend the combination of 
marks under the inexact scheme of a sum, or under the in- 
adequate, and still insufficient, picture of a product. If one 
of the numbers to be added is removed, this does not affect 
the other numbers to be added, and the sum is lessened only 
by the value of the number removed. If a factor is =0, then 
the whole product is =0. But the removal of an attribute 
ought neither to leave the other attributes undisturbed nor 
annihilate the whole. Both can happen in certain cases, but 
in general the other attributes are partly removed, partly 
modified by the removal (real, or thought to be real) of an 
attribute, and the whole is not removed with it. 

The expression Content has been formed after ἐνυπάρχειν." 
The expression mutual determination of attributes, which 
Lotze? uses to designate the dependence of the attributes on 
each other, would be convenient if the term determination 


were not already used in another cognate sense (see below, § 
52). 


! Arist. Anal, Post. 1. 4 : ἐνυπάρχειν ἐν τῷ λόγῳ τῷ τί ἐστι λέγοντι 
2 Log. p. 58. 


᾿ , > - Φ' ἃ 
or & VUMUPXELıV Ev To Tt ἔστιν, 


\ 51. Attention and Abstraction, etc. 





PART THIRD. 


THE NOTION ACCORDING TO CONTENT AND EXTENT 
IN ITS RELATION TO THE OBJECTIVE ESSENCE AND 


TO THE GENUS. 


$ 51. WHEN several objects agree in certain attri- 
butes and their conceptions in part of their content 
(δὲ 49-50), there may result the GENERAL CONCEPTION 
(allegemeine Vorstellung, Schema, notio sive represen- 
tatio communis, generalis, universalis). It arises by 
attention to the similar attributes and abstraction of the 
dissimilar, in consequence of the psychological law of 
the mutual arousing of similar mental (psychic) ele- 
ments and the reciprocal strengthening of the similar 
in consciousness. ‘The more general conception arises 
in the same way from several general conceptions which 


agree in part of their content. 


The general conception (in opposition to the individual con- 
ception) is not to be confounded with the abstract (in opposi- 
tion to the concrete, s. § 47). The divisions cross each other. 
There are concrete and abstract individual conceptions, and 
concrete and abstract general conceptions. The usage of some 
logicians, which identifies abstract and general, is not to be 
recommended. Grammar distinctly distinguishes the two. 


[! Cf. Mill’s Logic, 7th ed. i. 29.] 














128 


$ 51. Attention and Abstraction, etc. 





Wolff’s terminology agrees with the grammatical. He! defines 
the ‘notio abstracta’ as that ‘quae aliquid, quod rei cuidam 
inest vel adest (scilicet rerum attributa, modos, relationes) re- 
praesentat absque ea re, cui inest vel adest;’ but the “ notio 
universalis’? as that ‘qua ea repraesentantur, quae rebus 
pluribus communia sunt.’ 

Aristotle noticed that one experience embracing them all 
together in it may arise from several similar perceptions if me- 
mory preserves them; for the universal remains in the mind 
and as it were finds a resting-place there, and this universal is 
the one amongst the many, which dwells in the many as the 
same :—'Evovons δ᾽ αἰσθήσεως τοῖς μὲν τῶν ζῴων ἐγγίνεται μονὴ τοῦ 
αἰσθήματος, τοῖς δ᾽ οὐκ ἐγγίνεται. Ὅσοις μὲν οὖν μὴ ἐγγίνεται;--- 
οὐκ ἔστι τούτοις γνῶσις ἔξω τοῦ αἰσθάνεσθαι. ἐν οἷς δέ, ἔνεστιν 
αἰσθομένοις (or, according to Trendelenburg’s Conjecture, μὴ 
αἰσθανομένοις, The Codices have mostly αἰσθανομένοις without 
μή, one, D, ἢ μή) ἔχειν ἔτι ἐν τῇ Wuyn.— Ex μὲν οὖν αἰσθήσεως 
γίνεται μνήμη, ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομένης ἐμπειρία, 
ἐκ δὲ ἐμπειρίας ἢ ἐκ παντὸς ἠρεμήσαντος τοῦ καθόλου ἐν τῇ ψυχῇ, 
τοῦ ἑνὸς παρὰ τὰ πολλά, ὃ ἂν ἐν ἅπασιν ἕν ἐνῇ ἐκείνοις τὸ αὐτό, 
τέχνης ἀρχὴ καὶ ἐπιστήμης.Σ Aristotle calls Abstraction ἀφαέ- 
pecs. The opposite of abaipsoıs is πρόσθεσις... 

The functions of Attention and Abstraction, which were 
ascribed by earlier writers for the most part to the ‘ understand- 
ing,’ to a quasi-personifying general power, within the whole 
personality of the mind, have more recently by Herbart, Beneke 
[Hamilton and Mill] been reduced to psychological laws.® 


' Log. $ 110. 2 Ibid. § 54. 

$ Arist. Anal. Poster. ii. c. xix. 99 B, 36; De An. iii. 2, 425 B, 24. 

* Anal. Post. i. e. xviii. 81 B, 3; cf. De Anim. iii. 4, § 8, ibique 
comm. Trendelenburg. 

® De Coelo, p. 299 a, 16; Anal. Poster. i. c. xxvii. 87 a, 34. Cf. 
Plato's Rep. vii. 534 B: ἀπὸ τῶν ἄλλων πάντων ἀφελὼν τὴν τοῦ ἀγαθοῦ 
ἰδέαν, separating the idea of the good from all others. 

6 Cf. Berkeley’s remarks on Abstraction in the intreduction to his 


Prin. of Hum. Knowl., and note 5 to my translation. [Fraser’s edition 
of Berkeley’s Collected Works, i. 140 f.] 


N 51. Attention and Abstraction, ete. 129 





Herbart also rightly remarks that a pure separation of the 
like elements from the unlike may be a logical ideal, which can 
easily be postulated by ἃ definition, but can be actually realised 
only approximately by a process of abstraction. We determine 
to leave out of our consideration that kind of difference which 
is not connected with a certain course of thoughts, but it can 
never be quite rooted out of consciousness in the actual con- 
ception. The purest separation possible comes about when 
conscious scientific insight is superadded to the unconscious 
activity of the psychological law.' 

Before Kant’s time the grammatical rule in use was,—to 
abstract the common attributes. Thus, e.g. Lambert says,’ 
‘We abstract the common attributes from those which belong 
specially to each individual, in order to get at those which, when 
so abstracted, make a general or abstract notion.’ Kant! finds 
fault with this usage, and thinks the only valid expression 1s,— 
to abstract the dissimilar elements in the conception in order to 
attend to the similar. On his authority this latter rule has 
beconie the prevailing one, and cannot well be given up again. 
It is, however, open to the grammatical inconvenience that it 
does not agree with the procedure of the abstract participle, 
and to the actual defect that it lays too much stress on what 1s 
only an action of less importance. For (as Kant himself re- 
cognises) it is not the becoming unconscious of dissimilar ele- 
ments, but the concentration of consciousness on the similar, 
that is the essential thing in what is called the process of ab- 
straction. 

[Hamilton adopts the phraseology of Kant. He explains 
further that Attention and Abstraction are only the same 
process viewed in different relations—the positive and negative 
poles of the same act. He generalises the action of Attention 
and Abstraction into the rule, —Pluribus intentus minor est ad 
singula sensus. The points of resemblance among things are 
discovered by Comparison, and by Attention constituted into 


1 Cf. I. H. Fichte, Grundzüge zum System der Philosophie, 1. Abth. 


Das Erkennen als Selbsterkennen, § 86 ff. 
2 N. Org. i. § 17. 3 Log. ed. by Jiische, p. 146. 


K 

















139 ὃ 52. Determination. ὃ 53. Extent. Division. 





exclusive objects; by the same act they are also reduced in 
consciousness from multitude to unity; for objects are the 
same to us when we are unable to distinguish their concep- 
tions.!] 

The process of Abstraction is reciprocally related to the 
designation of many similar objects by the same word. This 


sameness of designation is possible by the process of Abstrac- - 


tion, and the result of this process is itself secured and made 
permanent by the sameness of designation. Extreme Nominal- 
ism is wrong, however, when it seeks to reduce the process of 
Abstraction to a mere identity of verbal relation. 


§ 52. DETERMINATION (πρόσθεσις) means the forma- 
tion of less general conceptions out of the more general. 
The content of these last is increased by the addition 
of new elements of conception appropriate to the object 
conceived, and what remained undetermined in the 
more general notion becomes more closely determined 
(determinatur). The formation of new valid con- 


ceptions implies an insight into the real relation of 
dependence among the attributes. 


Subjectively-formal logic, from the essential demand of its 
principles, is not able to lay down the rule, that, in the addition 
of new elements of content, reference must be had to the real 
relation of the characteristics to each other and to the whole. 


§ 53. The zexrewr (Ambitus, Sphaera, sometimes 
extensio) of a conception is the totality of those concep- 
tions whose similar elements of content (cf. ὃ 50) make 


! [Lect. on Logic, i. 123 ff.; ef. Lect. on Metaph. i. ; cf. Mill. Exam. 
of Sir Wm. Hamilton’s Philos. örd ed. pp. 364 ff.; Mansel, Proleg. 
Log. 2nd ed. p. 65, where he distinguishes, as above, the unconscious 
psychological process from the conscious scientific procedure. 


? As Hobbes did; see Computatio sive Logica, ¢. ii. ; 


Leviathan, 
pt. i. ch. iv.] 


The Relations of Conceptions to each other, etc. 131 





up its content. The enumeration of the parts of = 
extent of a general conception is called Drvistow : Ji- 
visio). The general conception, in relation to : ΕΠ 
conceptions which fall within its extent, is the Bi ven κὴ 
superordinate ; they in relation to it are the ower Ὁ 

subordinate (Relation of Subordination). ÜREREINEE 
which are subordinated to the same higher one are ¢0- 
ordinate (Relation of Co-ordination). Aequipollent or 
Reciprocal (notiones aequipollentes or rn. = 
ceptions are those whose spheres are identical with each 
other, without their content being exactly the oat 
Identical conceptions have the same extent and content. 
Those conceptions are opposed to each other εν τον 
traries (notiones contrarie oppositae) which, wit in = 
extent of the same higher notion, are most Euer 

from each other, and furthest removed from each 
other when both have a positive content; when 
notion contains only the denial of the Be of = 
other, both are said to be opposed to each ot er 
as contradictories. A notion which merely seni is 
called notio negativa seu indefinita (ὄνομα ἀόριστον, Pe 
ἀόριστον). The Spheres of different notions se = 
when they fall partly within, partly without each o εὐ 
Conceptions are compatible (notiones inter se - 
venientes) when they can be combined in the con 
of the one and the same conception (consequently * en 
their spheres fall wholly or partly within each other ); in 
the opposite case, they are incompatible. — are 
disjunct when they fall within the extent of the a 
higher, especially if it be the next higher, .. > 
(and consequently have some identical elements of coI 

k 2 











132 ὃ 53. Extent. Division. Relations of Conceptions 





tent), but have no part of their own extent common (and 
consequently are not combined in the content of one 
and the same notion). They are disparate, on the other 
hand, when they do not fall within the extent of the 
same higher, or at least of the same next higher, con- 
ception (and consequently have not common elements of 
content), while they sometimes have a part of their own 
extent common (or are combined in the content of one 
and the same notion). All these relations of concep- 
tions exist not only in substantive, but also in verbal, 
adjectival, and relative conceptions. The formal rela- 
tion of the subordination of several conceptions under 
the same higher one leads to the notion of number, which 
is originally (as whole number) the determination, by 
means of the unit, of the plurality of the individuals of 
the extent. 


Geometrical figures, especially the circle (Ellipse, &e.) and 
parts of the circle, serve as a very convenient aid for the clear 
representation of the relations of extent. 

The relation of subordination between the conceptions, of the 
superordinate A (e.g. man) and the subordinate B (e.g. Euro- 
pean), is illustrated by two circles, the one of which falls wholly 
within the other :— 


A 


The Co-ordination of two conceptions, A and B, both of which 
are subordinated to a third, c (e.g. A=valour, B= prudence, 
c=duty), is illustrated by the following figure :— 


ὉΪῸ 


to each other according to Extent and Content. 133 





In Aequipollence the two circles coalesce. The spheres are 
denoted by A (e.g. foundér of scientific Logic), and by B 


(e.g. tutor to Alexander the Great) :— 


The relation of contrary opposition between A and B (e.g. 
white and black, or in reference to the widest difference in the 
circle of colours, red and green, yellow and violet, blue and 
orange) may be expressed in the following way :— 


In ‘contradictory opposition, between A and non-A (e. δ᾽. be- 
tween white and not-white), the positively definite notion A 1s 
denoted by the space of the circle, the conception B or non-A 
is negatively definite, but with reference to its positive content, 
left indefinite by the unlimited empty space outside the circle :— 


The relation of Intersection between the conceptions A and 
B (e.g. negro and slave, Apocrypha and ungenuine writings, 
regular figures and parallelograms, red and bright) is sym- 
bolised by two intersecting circles :— 


The schema of the Compatibility (e.g. red and coloured, 
redness and colour of the smallest number of the vibrations 











134 § 53. Extent. Division. Conceptions, ete. 





of aether, redness and brightness) is made by combining the 
schemata for Subordination, Aequipollence, and Intersection. 

The schema for Incompatibility (e.g. red and blue) is the 
complete separation of the circles :— 


Disjunct conceptions (e.g. Athenians and Spartans, motion 
and rest) belong to opposing ones. They are only distinct 
because they are comprehended under one and the same higher 
conception. Their schema is therefore :— 


O® 

There is no sufficient schema for the relation of disparate 
exceptions (e.g. spirit and table, red and virtuous, long and 
sounding ), because the negative determination, that their spheres 
do not fali within the extent of any conception superordinate 
‘commonly to both (excepting of course the quite general and 
indefinite conception of Anything), cannot be represented by a 
figure. The positive relation of their spheres, however, re- 
mains so far indefinite, that it can be that of intersection or 
that of complete separation. 

The relations of judgments and inferences may be symbolised 
in a similar way: see under $ 71; ὃ 85 ff.; §105 ff; and for 
the history of this symbolising cf. § 85. 

For the corresponding doctrines of Plato and Aristotle, cf. 
δὲ 51 and ὅθ. According to Plato the individual good has part 
in (μετέχει) the idea of the good, the individual beauty in the 
idea of the beautiful, and so every individual in its correspond- 
ing idea. Within the world of Ideas, according to the author of 
the Sophistes,' the lower (the logically subordinate) is compre- 


1 Soph. Ρ. 250 Β. 


§ 54. Relation between Content and Extent. 135 





hended (περιέχεται) by the higher. With Aristotle the more 
universal is the πρότερον φύσει (cf. ὃ 139). He uses the ex- 
pressions, πρῶτος, μέσος, and ἔσχατος pos! of notions which 
stand in the relation of subordination, and says of the sub- 
ordinate notion, in reference to its extent, that it is wholly 
comprehended in the higher, or included in it (ἐν ὅλῳ εἶναι 
τῷ μέσῳ.--τῷ πρώτῳ, and so on). The representation of the 
relations of conceptions by means of circles is connected with 
these Aristotelian expressions. It was first applied in the 
Nucleus Log. Weisianae, 1712, written by J. Ch. Lange. Cf. 
§85. For contrary opposition cf. (Plat. ?) Soph. p. 257 B, where 
ἐναντίον and ἕτερον are distinguished; Aristotle, Metaph. x. 4, 
where the opposition is defined to be the μεγίστη διαφορά be- 
tween species of the same genus. The Aristotelian expres- 
sion,? ἐστὶ μὲν ταὐτό, TO δὲ εἶναι οὐ ταὐτό, refers to conceptions 
of the same extent but different content. The expression 
disjunct is connected with the Aristotelian ἀντιδιῃρημένον. ὃ 
and more closely with the later term διάξευξις (cf. § 123). 

[ Hamilton supplemented the list of relations of conceptions, in 
reference to their extent, by a list of their relations in reference 
to content. The great stress he laid upon the equal importance 
of content and extent in logical forms led him to make the two 
lists as far as possible parallel. The relations in content cannot 
be symbolised by figures. Hamilton’s list is chiefly taken from 
the Logics of Esser and Krug.‘ | 


§ 54. The higher conception has a narrower content 
but a wider extent than the lower; for it contains 
only those elements of content which agree in several 
lower conceptions. The lower conception has a fuller 
content but a narrower extent. The extent, how- 
ever, is by no means increased or lessened by every 
lessening or increase of a given content; nor, on the 


1 Anal. Pr.i.1,4. 3. Eth. Nic. v. 3, 1130 a, 12. 3 Top. vi. 6. 
4 (Cf. Lectures on Log. i. lect. xii. 








| 


| 














136 ὃ 54. Relation between Content and Extent. 





other hand, is the content increased or diminished 
with every decrease or increase of a given extent. Still 
less does the law of a strict inverse ratio [as Hamilton 
says] regulate those cases, in which the decrease of con- 
tent produces an increase of extent, and an increase of 
content a decrease of extent. 


[Hamilton asserts expressly —‘ these two quantities of com- 
prehension (content) and extension (extent) stand always in an 
inverse ratio to each other; for the greater the comprehension of 
a concept the less is its extension, and greater its extension the 
less its comprehension.’ "] 

Drobisch? seeks to express mathematically the relation 
which exists between the increase of the content and the 
decrease of the extent. He proves that the content is not in 
the inverse ratio of the extent, but that other relations exist. 
He shows (to mention only the most important) that, under the 
simplest presupposition—i.e. when in the series of subordinations 
the number of conceptions, which are immediately subordinate 
to any one or are richer by one element of content, is always 
the same, and when, at the same time, the extent is mea- 
sured exclusively according to the number of the concep- 
tions of the lowest rank—the size of the extent decreases 
according to geometrical progression, while the size of the con- 
tent increases according to arithmetical progression. Drobisch 
further expresses this theorem by these two other assertions. 
On the above presupposition, the extent of a conception is 
inversely proportional to that power whose base is formed by 
the number of conceptions immediately subordinate to any one 
conception, and whose exponent is formed by the number of 
the elements of the contents of that notion. Under the same 
presupposition, the difference between the greater number of 
elements of the content of one of the lowest conceptions, 
and the (lesser) number of the elements of the content of any 


! [Cf. for a thorough discussion of the matter, Lect.on Logic, i. 146 ff. ] 
? Logik, 2nd ed. pp. 196-200. 





ıxtent. 13 
§ 54. Relation between Content and Exten 37 





— 


is di i the logarithm of the 
directly proportional to 
rf a ent size of the extent. The 


h is valuable as a mathe- 


conception, 
number which expresses the pres 


f this investigation (whi 
u loctes ion) i dered useless in most cases, by 
matico-logical speculation ) 1s rendere 


the circumstance that peculiar limitations, which eens 

| | . νει. . . 4 - 

brought under general rules, underlie the possibility of attr 
δ 


isti ° xample: 
butes existing together. For examp 


(Rectilineal) Triangle 
right-angled | obtuse 


m | isosc. scal. | (equilat.) isosc. scalene. 


equilat. | isose. | scal. | (equilat.) 


} = .=I9I= 
Drobisch computes as follows: Triangle, cont. = eee ᾿ 
32, Acute triangle, cont. ΞΞ ἃ + l, ext. =3=3'. quis ie ἢ 
, t =a+2,ext=1=3°. But this computation 1s ἊΝ 
cont. = , ext. = = | COr | 
nary, because two of the nine combinations are ” = . : 
in to the geometrical relations of er e nn 
᾿ tri 4 ions 
triangle. Where concep 
the sides and angles of a ang nee 
to natural objects and relations of mental (geistige) life, the 
icati is still more limited. 
lication of these laws 1s sti . ; 
"The universal conception adjusts itself? > a 
tal features only, in whic 
ll marked in some fundamen ly, in 
pate et do not waver in the Whole; but in the nn pee 
out 
᾿ς room for a freer play of the phantasy which fills in the = 
ἣ The common picture within the fundamental out > 
ste imit, 1 i d can take a manıfolc 
| kes its limit, is elastic and ife 
cea If we call? this indeterminateness and elasticity 


of attributes or generalities of attributes, indefinite 
numerous as those embraced 


formation. 


a quantity 
but able to be made definite, as 


1 In the 3rd ed. of his Logik (p. 211), Drobisch expressly ee 
tl jaime holds good only on the presupposition that a — - > 
"a | ific difference of the Io 

d by every specific di 

order is to be determinec y ΡΣ PIES 

It is true that this presupposition 18 somet! shes 

f . Subjectively-formal logic, as 

‘« realised completely in very few cases ΕΞ ve 

5 ch ge ri into consideration the limited validity of the presup 
such, cé ; te 


‚osition, for that depends upon real relations of Ben τ ὩΣ 
: 2 Trendelenburg, Log. Unters. 2nd ed. il. 220 ff.; 3rd ed. 1. 


3 With Lotze, Log. pp. 71 ff, 79. 


order. 














128 ; 
3 δ 55. ‚Series of Conceptions. 





in the lower conception, definitel : 
opposed to t - y and simply; then, there st 
Bic Sh = = doctrine, that the higher conception Key 
Fi Boten 2 a content, the new doctrine, that 
content of the low igher conception does not come behind the 
certain degree of = in number of attributes; and this has a 
and not to be a ae = terminology is artificial, 
in referen content must manifest i 
ite ren 2 ig way in which a 
= : ee g the exten 
re ae ee of thoughts around > ei pied 
ing “the ae not by extending but b i = 
re ae 4 unsettled possibility. The sum Migs 
ee wage se contained only potentially in ‘as 
the entrance of oth cir actual existence is accomplished b 
things, besides thi er elements. There are in the REES 5 
attribute with a ee specific connection of a ee 
en into which an re ee 
he smalles . on attribute can 
‘ta ET of (logical) elements of been 
tent, only potenti lly or attributes corresponds to the widest ; 
(in the individu . asserted ; the greater number, to a Be 
nd “in tas st to the smallest) extent, actuall d 
a es — possible has to do with act 
ih canteen ee, == ai. the greatest number of al 
a ee > be > individual conceptions. [ Cf. also 
connotative and denotative pits et a upon 
Ψ πὸ . 


55. $; ᾿ 
πὰ on = relation of subordination and of super- 
nn seis continuously by an abstraction 
een i ns simple content is reached, the 
oo apie conceptions can be thought of. =“ ar- 
᾿ - sa ing to the relations of extent and = t 
organic gradual succession. The summit or aaa 
er 


I As Trende U, 
As Trendelenburg demands, Log. Unters. 2nd ed. p. 226 
d. p. ff. 


§ 56. Definition of the Notion. The Essence. 139 


limit is found by the most general conception something. 
Immediately under it lie the categories. The basis, or 
under limit, is formed by the infinite number of indi- 


vidual conceptions. 


The gradual successio 


Pyramid. But this pieture is on 
the subordination of conception is not carried on with striet 


uniformity. The highest conception is not the conception of 
(Etwas), because Being falls 


Being (Sein), but of Something 

under one of the Categories, viz. under that of Attributive 

(predicative) Existence, and is opposed to Being as substantive. ~ 

Something, on the other hand, comprehends all the Categories 

(an action or passion, property or relation, as, e.g. by, near to, 

&e., is Something). The highest material opposites, such as 
ected with the 


Real or Ideal, Natural and Spiritual, are conn 
Categories, which are the highest formal divisions. They are 


divided according to anot 
themselves in every one of the Cat 


orion (Begriff, notio, conceptus) is that 
h the sum total of the essential attri- 
(Wesen, essentia) of the object 


is conceived. By the phrase— 
of the object, we include not 


hich it is known, but all its 
and relations,—in short, 














n of conceptions may be compared to a 
ly approximately true, because 


her principle of division, and repeat 


egories. 


§ 56. The Ν 
conception in whic 
butes, or the essence 
under consideration, 
attributes (Merkmale, notae ) 
only the outward signs by W 
parts, properties, activities, 


whatever belongs in any way to the objec 
(essentialia) are those attributes which (a) contain the 


common and persistent basis for a multitude of others ; 
and on which (Ὁ) the subsistence © 


and its meaning, depends. 


partly because it is a means 
partly and principally to itself, as a final end in ἃ 


oradual course of objects. 








t. The essential 





f the object, its worth 


This meaning belongs to it 
to something else, and 


In a wider sense also, 


140 $ 56. Definition of the Notion. 








these attributes are called essential, which are neces- 
sarıly united to marks essential in the stricter sense, 
and whose presence, therefore, indicate with certainty 
the presence of those others. The essential charac- 
teristics, in the strictest sense, are called the funda- 
mentally essential (essentialia constitutiva); the others, 
which are only essential in a lower sense, derivatively 
essential (essentialia consecutiva) or attributes in the 
stricter sense (attributa). The other characteristics of 
an object are called non-essential (accidentia, modi). 
The possibility of modi or the capability to take this 
or that modification must have its foundation in the 
essence of the object. Under the essential determina- 
tions are those which the notion has in common with 
notions super-ordinate and co-ordinate with it, the 
common ones (essentialia communia), and those by 
which it is separated from these notions, the proper or 
peculiar (essentialia propria). The relations belong 
generally to the non-essential, but with relative notions 
they are essential attributes. In the proportion that the 
fundamentally essential characteristics are unknown, 
the formation of the notion is ambiguous. With another 
grouping of the objects, other determinations may ap- 
pear to be common and essential, and the whole pro- 
cedure cannot raise itself above a relativity which rests 
on accidental subjective opinions. In proportion, how- 
ever, as the really essential characteristics are known, 
the conceptions acquire a scientific certainty and an 
objective universal validity. In perfect knowledge 
notions are valid only as they correspond to the types 
of the real groups of their (natural or mental) objects. 


The Essence. 141 








— 


‘on is not made in the purely 
τρίτοι = ee a by any external rn 
scientific ge ‘ urpose of a superficial view of any 
in Ἴ nie jane which has for its aim the wides el 
yer τῶν the most essential. Several age — 
yr τρία, "ἢ otion can exist alongside of each other, - z 
Nae as han pet relatively correct ; one only, howev > 2 
ee t, that, viz. which constructs the no νέμι 
ker objective laws, on the basis of what 1s n 
urely a g to object | 
cent - γα ee shown that he was =. 
] gi ie Be in knowledge, = en 
mi ject of notiona odg 
er τ τρὶς = = epee εἶδος), aad strictly distin- 
He define 


h the notion, 
guished the real thing, 


y b 


le 
᾿ Κ in vain throughout the who 
hese here εἶδος or 
ngle passage where 
e notion, or where this 


ne 1 
1 1 inds. 
icture in our mM 
. . si 

of Plato’s writings for one 


jecti rrelative to the subjective notion. 
2. epi Sn ee this ee 
He failed m in things, he hypostatised wid obj oa 
essence In ne of things and separate from them : ah ze 
cn he ascribed to the idea an existence = En 
pani ops μοι The Platonic dovtrine of Ideas 15 the to 
dent and io A 


. 27 pv, 29 C, 
A es 3 566. 5 Tim. pPP- τ 
‚509 sqq., vii. 53 d in the 
DET: 2 N 14. The Parm. p. 182 », Ps elation of the 
37 B, C, ol εὐῇ πὰς It represents very clearly = Se It cannot, 
first ed. = nn of notional knowledge " weeps sali to prove, 
u to eS a a proof of Plato’s views, if, as I eg . 175-184, 
e “ : ; 
however, _— is not genuine. Cf. Plat. — z ae Phil. 
en d Ueber den Dial. Parm. in the Jahr eae d Politicus 
Wien, aap ΟΝ 1864). The genuineness of the ge Mus. ἢ 
(p. 97 ff., Leip. idt has shown (in the Zehen. TuS. J 
Schaarschmi . Ueber die 
ET cn Banden, vid. yp. 1-96 MB N 1864; Ue 
hilol. New ’ ς 1- . 
nl Schriften, Bonn, 1866, pp. 18 








142 § 56. Definition of the Notion. 





u 


shadov ine ° 
on ais peng es home truth in a mythical form. 
anthropomorphic sods of ir ae RER ideas to the 
aia: ῬΝδ κὼὰ x 2 yt ology.? Aristotle battled against 
are. oe ew O ideas, 1.e. against the supposition that 
ehr =. separation from the individual existences as 
real correlate t oe ne = does not reject the doctrine of a 
eee : o the subjective notion. He did not place th 
of thought outside of all relation to the forms = we 


He recogni 

nised i i 
wer a τῇ ῥα thorough-going parallelism between both (cf. 
sia : -ording to Aristotle the essence corresponds to tl 

J { : f 

‚and is therefore called by him ἡ κατὰ λόγον οὐσί The 

essence is im i indivi er “a 
aes manent in the individual existe 1 
says*—eidn μὲν οὖν εἶναι ἢ ἕν τι παρὰ τὰ er 
: apa τὰ πολλὰ οὐκ ἀνά 
z i ἃ οὐκ ἀν = 
ἐ αι μέντοι Ev κατὰ πολλῶν ἀληθὲς εἰπεῖν ἀνά eine 
εἴδεσι τοῖς αἰσθητοῖς τὰ νοητά ἐστιν τ αι". 


This one in th . 
e many, this intelligible i 
: e in tl : . 
called by Aristotle the form, the διε ie, ἐδ τιν En = 
3 » Wi ἃ ter- 


uP 
unology quite peculiar, the being what a thing 
w 


4 ς P , 
εἶδος, ἡ κατὰ λόγον οὐσία, τὸ τί ἐστι as— μορφή. 
9 


; and τὸ τί > ᾽ 

expression τὸ τί ἦν εἶναι] . τὸ ἣν εἰναι. The 

τί ἣν εἰναι is explained by Aristotle himself t 
ie 0 


be 
the term for the matterless essence.® τὸ τί ἦν εἶ 
. Ὁ Ti ἣν εἰναι Corre- 


1 Met. iii. 2, 997 8, 10. 


2 It is an apprehension historical] i 
with Plato’ ᾿ ally true in the main, and agreei 
ae aa nae ee especially in his ἴα: ee 7a 
ie nis woher it (Ritter, Gesch. der Philos. iii. 120 “1831 
ntatioed by en zus em when Aristotle thinks that ideas ‘ie hy > 
Aristotle has ony ἀοβηοᾶ, enge from the sensible Pe 
conception re dogmatically than it is i 
ed jas nz Σ oa , the See which in ei 
ua ae ativeandreal meaning. He has done it in strict 
En iin er = later constructions and with the doctrine 
De 2 ger ne desire to combine philosophy with poetry, whi h 
en a Me generalisation finds to be the ia 3 
οὐδν ἐδ Ῥιωκοδο xe se hilosophy, 1s certainly the characteristic ned 
Ea 2 zur ation, but also of Platonic thinking. Aristot] 
endation, not blame, when he in his own ee 2 
Tip 


Oo y SICH τ 


4 na . : . } 
| { J I 4 7 . V ll. 7 . 


The Essence. 


sponds, therefore, to the abstract form of the notion (and con- 
sequently to the substantivum abstractum). (Cf. in this 
reference the difference, explained by Plato in the dialogue 
Phaedo,! of the inherent characteristic from the thing in 
which it inheres.) It does not, however, amount to the mere 
general characteristic of genus, still less is it concerned with 
the non-essential qualities. It is the whole collected essen- 
tiality (everything which must enter into the definition ), 
and includes both the characteristics of the genus and the 
specific difference. The τί ἐστι of Aristotle is of wider and 
less definite use. It can denote both the matter? and the 
matterless essence,? and, lastly and most eommonly, the union 
of the two, the σύνολον ἐξ εἴδους καὶ Ühns.! In this last case it 
corresponds to the concrete form of the notion (and so to the 
substantivum concretum). The non-essential determinations 
or the mere accidents (συμβεβηκότα), 6. g. mere qualities (ποιά) 
or quantities (rood), cannot serve as answers to the question 
τί ἐστι; at least, not when, as usually happens, the question is 
about the τί ἐστι of a thing. Aristotle recognises, that not only 
with things (substances), but also with Quantities, Qualities, 
Relations—in short, in every category— the question τί ἐστι 
or the ri ἣν εἶναι can be asked, and the essential separated from 
the non-essential; but he teaches that the τί ἐστι is present 
in things in an original and pre-eminent way. In dependent 


existences (in the συμβεβηκότα) it is present only derivatively :° 
ἐκεῖνο δὲ φανερὸν ὅτι ὁ πρώτως“ καὶ ἁπλῶς ὁρισμὸς καὶ τὸ τί ἦν εἶναι 
τῶν οὐσιῶν ἐστιν. οὐ μὴν ἀλλὰ καὶ τῶν ἄλλων ὁμοίως“ ἐστί, πλὴν 
οὐ πρώτως. By this remark the two meanings of οὐσία, Essence 
and Substance, are placed in inward relation to each other. 
Unfortunately, however, the number of the meanings of this 
word, which denotes—now Substance in the sense of substrate 
or material basis of existence (τὸ ὑποκείμενον OF ἡ ὕλη; sub- 
jectum); now the essence corresponding to the notion (ἡ κατὰ 


λόγον οὐσία, εἶδος. μο 1, τὸ τί ἦν εἶναι, essentia) 5 NOW the whole 
Y ’ ἢ N 3 


2 E.g. Metaph. viii. 3. 


1 Phaedo, p. 193 8. 
4 E.g. Metaph. viii. 2. 


3 E.g. De Anima, p. 403 a, 30. 
5 Ibid. vii. 4. 





ὲ un 
44 § 56. Definition of the Notion. 
or N φ \ 4 \ > = i 
"ΕΑ = en an τὸ ἐξ ἀμφοῖν, ens), and in this third 
Ἢ the individual existence (τόδε τι, indivi 
ndividuum) and th 
sum total of the obj = 
jects belonging to one & 
= ὅν: | ging genus, or to one 
ας (m on TO εν genus, species, materialiter sic dicta) 
—trom then till now has been the cau 
se of numberless c 
vagueness and error. A defect sti an 
. ct still more felt lies in thi 
| in this, th 
— en. there are no criteria of Essentiality The ai 
erence often brought forward i 1 : 
g in the treatise on th 
” e Categories 
zur belongs to the essence can be predicated of the 
er er " on be in the subject, while the accident is in 
ject (e.g. Socrates is man, b i 
er t (e » but man is not in him: 
re Is wise, and wisdom is in him), is not a 
- sd s ient. 
2 " aces the opposition of substantive and adjective 
ppre _—n of the predicate notion for essentiality and non 
see Now the two divisions are not parallel, but pene 
ch other (e.g. Socrates is gi 
g s is gifted with lif 
é 4 15. g ite and reason; 
. is a wise man). Aristotle, not usually, nor yet in his 
a _ writings, but now and then in single places, mak 
ε . . . = " 
= —— hold good for essentiality and non-essentialit 
: at > an essential part of the whole whose removal or 
: a 5 uences the whole.! But here, of course, the amount 
u > the totality of the remaining parts remains 
ee = ce = = the definition belongs, in its totality 
ject of the definition onl ut 
y, or is peculiar to-it; 
aa parts of the definition may belong to other Pi: 
. . = 8; 
an aes the essence given in the definition anil Is 
. . £ 
— be peculiar to the object of the definition. This a 
i . n the narrower sense.’ Predicates which follow nec : 
arily from the essence are called συμβεβηκότα ταῖς οὐσία by 
ıs by 
I ὥστε μετατιθεμέν D 3 
ὃ sere μένου τινὸς μέρους ἢ adaıpov Evov διαφέ N 
κινεῖσθαι τὸ ae) Poét. c. viii. 1451 a, 33; πω uaa. ie 
ΓΝ gr ἢ μὴ προσὸν μηδὲν ποιεῖ ἐπίδηλον, μηδὲν is the pee, 
κι er f. my translation of the Poetics, Berlin, 1869 το. a 
°?.- vi. 12: ἐκάστον yap τὸ βέλτιστον ἐν τῇ οὐσί én Er > 
Anal. Post. ii. 13. Sen 
Ὁ 277 
Top. i. c. iv. 101 B, 22; ibid. c. v. 102 a, 18. 


The Essence. 145 











Aristotle,! or (more commonly ) συμβεβηκότα καθ᾽ αὑτό. 
These last were later called the consecutively essential or 


They too belong to the καθόλου ; for the καθόλου 
t is denoted in the whole 


ὑτό), 


The 


2 


attributes. 
is everything? which belongs to wha 
extent of its notion (κατὰ παντὸς and καθ᾽ αὑτὸ or 7 α 
in distinction from what is common in any way (κοινόν). 
καθόλου is ἃ κοινόν, but every κοιὐνὸν Is not a καθόλου. 
According to the doctrine of the Stoics, notions exist 
only as subjective creations in the mind. The κοινὸς λόγος, 
the reason of the universe separated into a plurality of 


λόγοι, dwells in external things. But the Stoics do not ex- 
pressly make these λόγοι denote what is known by the sub- 
jective notion. 

In the Middle Ages the Realists paid homage partly to Plato, 


and partly to Aristotle’s opinions,—* universalia ante rem,’ and 
The Nominalists allowed no other ex- 


ersalia’ (universal objects or universal 


predicates) than an existence in the word (strict Nominal- 
ists), or in the thinking mind also (Conceptualists)—* Uni- 
The manifold defects in Platonic and 


lled forth Nominalism, its extreme 
Among modern 


‘yniversalia in re.’ 
istence to the ‘ univ 


versalia post rem.’ 


Aristotelian Realism ca 
and gave a relative correctness to it. 
Leibniz, as well as Bacon and Locke, 


belong to Nominalism, or rather to Conceptualism. This 
logical and metaphysical problem, discussed by Scholasticism, 
was scarcely affected by the psychological question, chiefly 
discussed by modern philosophers, about the origin of our 
notions, viz.—Are notions really innate? Is development in 
common life limited to a gradual coming more and more dis- 
tinctly into consciousness? or, are all notions, in content 
and form, products of a mental development conditioned by 
outward influences? Kant and Herbart, like the earlier No- 
minalists, concede to notions ἃ subjective meaning only. 


opposite, 
philosophers Descartes, 


1 De Anima, i. c. i. 402 B, 18. 
2 Metaph. v. c. xxx. 1025 a, 30: ὅσα ὑπάρχει ἑκάστῳ καθ᾽ αὑτὸ μὴ 
ἐν οὐσίᾳ ὄντα. 

3 According to Anal. Post. i. 4. 


L 








Boe 


Sa eS anne nnn Tu 


146 § 56. Definition of the Notion. 





Herbart uses “ universalia’ to denote all general and individual 
conceptions, so far as they are looked at, not on their psycho- 
logical side, but in reference to what is represented by them. 
Yet Herbart says,! in a passage where he is not expressly 
teaching Logic, but makes a logical remark accidentally— 
‘Definition becomes a significant expression of the result of 
this whole deliberation only after the first attempt to separate 
the essential from the accidental.’ Now, since the notion is 
determined by what is essential, and not what is essential by 
the notion, there is here presupposed a difference of the essen- 
tial and accidental lying in the objective reality, and the 
dependence of the genuine formation and explanation of 
notions—i. e. a formation and explanation, which corresponds 
to scientific and didactic laws—upon this objective difference 
is recognised. 

Subjectively-formal Logic, which should identify the notion 
with the general conception, so far as it at all explains the cate- 
gory of essentiality, calls those attributes essential without 
which an object could not be what it is, nor remain what it is, 
nor be subsumed under the same notion. In other words, 
those attributes are essential which belong to the object in the 
whole extent of its notion or make up its content.2 This ex- 
planation is unsatisfactory, for it argues in a circle. The 
notion is explained by the essence, and then the essence by the 
notion. If Logic? is to settle the normal laws of thought, it 
must answer the question,—according to what marks are ob- 
jects to be grouped together and their notions formed? For 
example, are plants to be grouped according to the shape and 
divisions of the corolla (Tournefort), or according to the 
number of their stamens and pistils (Linneus)? They are 
to be grouped: according to their essential attributes. What 
attributes are essential? Those which belong to the object 


! In his discourse at the opening of his Vorlesungen über Pädagogik, 
1803. Werke, Bd. xi. 63, Leipzig, 1851. 


2 Cf. Drobisch, Log. 3rd ed. ὃ 31. [Sir Wm. Hamilton’s account is 
the same; cf. Lect. on Logic, i. 217.] 


3 According to Drobisch, Logik, § 2. 


The Essence. 147 





in the whole extent of its notion, those which he in its ae 

and to which the name belongs. If then we seek first = 
correct notion and name, how shall we determine ᾧ a y 
the essential attributes. What are the essential! ose 
which lie in the notion; and sic in infinitum. The sage iti 
is, that the formation of the notion remains —- ses 
He who arranges plants according to the shape and wae’ 

of the corolla, and thereby forms his botanical noe or 
him the shape and Givisions are essential. He who νει. ἡ 
them according to size—for him size 1s essential; anc er ss 
At the best, the common use of words, as yet ones y 
science, gives a starting-point ; no way 18 pointed = ge ai 
are leftto the most elementary and wholly unscienti emo ar 

forming notions.! When we once know what — in 
ing to their nature, belong to each other, an er e εν» 
extent of the one and the same notion, we can se — 
right by this, in our search after the essential properties. " 
how can we scientifically know that reciprocal dependence, an 

determine rightly the limits of the extent, so long “in 
unable to distinguish the essential from the non-essential a tri- 
butes? Does the whale belong to the extent of the notion 
fish? Isthe Atomic philosophy within the sphere of pean 
of Sophistic? Does the mode of thought shown in the seu 2 
Clementine Homilies fall within the sphere of the notion 0 


1 Drobisch confesses this in the third edition of his pee ik 
remark appended to § 119 (p. 137), inasmuch as he —— = . 
distinction can only be fully justified and established when t : re eR 5 
is to the analytical definition of a notion which is nes Υ its wood 
monly used designation, when we only seek the notion " ne : — 
to a given name. But my assertion pans to this, t gen zu 
formal Logic, unless it goes beyond its principle, can only ring = ὁ 
its laws for the solution of certain merely elementary and ge > ῃ 
problems, and can only produce a small part of the nec potty τ 
and not, as is promised in Drobisch’s Logic (3rd δε § P- » oH 
normal laws of thought. The consideration of the ‘synt netic = 
of thought’ can only be scientifically satisfactory when " 2 = 
on the relation to the forms of existence (e.g. of the ground of kn 
ledge to the causal relation, of the notion to the real essence). 


Ὁ 








148 § 56. Definition of the “Notion. 








Gnosticism ? Does Joannes Scotus (Erigena) belong to the 
Scholastics? Tiedmann says '—* Scholastic philosophy is that 
treatment of objects 4 priori, where, after statement in syllo- 
gistic form of the greatest number of reasons for or against, 
decision is made from Aristotle, the Church Fathers, and the 
prevailing system of belief.’ It follows from this definition 
of the notion that Scholasticism proper had its beginning at 
the commencement of the thirteenth century, after quiches 
with the metaphysics, physics, and ethics of Aristotle, which 
did not take place until the close of the twelfth century 
(before this the Logic only was known). Whether this de- 
finition of the notion is to be agreed to, can be settled only 
from a consideration of the essentiality of the attributes, inde- 


pendent of the previous settlement of the extent. Every ques- 


tion of this kind can only be settled scientifically, when, before 
and independently of the limitation of the extent, the essen- 
tiality, or degree of the essentiality, of the attributes has been 
settled. Now, wherein lie the criteria? Subjectively-formal 
Logic, when it takes the forms of thought apart from their re- 
lation to forms of existence, and will not treat them as forms 
of knowledge, proves itself to be inadequate to give rules for 
that formation of notions which the positive sciences require. 
| The somewhat common explanation of the essential attri- 

butes as the lasting and persistent properties is not more satis- 
factory.” In its reference to the amount of time of duration 
this definition does not prove a just one. The highest jr 
most essential form, the most pre-eminent, is often the point 
of culmination of a life which swiftly passes away. If it only 
denotes inseparability from the object, so long as the object 
remains what it is, or while it is subsumed under the same 
notion, and can be called by the same name, the reasoning in a 
circle again results. 5 

The principle of grouping objects together according to the 
most important properties, or those which are of the greatest 
similarity or natural relationship (on which Mill? would 


1 Geist der spec. Phil. iv. 338. 


2 E.g. in Ritter’s Logik, 2nd ed. p. 67. 3 Logie, ii. 264. 


The Essence. 


149 








base the formation of notions), leaves the question undecided. 
For, What similarity or relationship is the greatest ? Α 
similarity in many, and even in most, determinations would 
by no means justify comprehension together and subsump- 
tion under the same notion, provided that the many were the 
least significant. A similarity in the significant, important, 
and essential would. But then we come back to the question, 
What are to be considered the essential ? 

H. Taine’s definition of the essential characters is to be cri- 
ticised in the same way!:—* The essential characteristic is ἃ 
quality from which all the other, or at least most other quali- 
ties, derive according to a settled mutual interdependence.’ 
The genetic consequence, without regarding the degree of value 
of each attribute, is scarcely sufficient for the determination of 
what is essential. Besides, one moment of an object ought 
not to come from another, but the sum total of the attributes 
from earlier original circumstances. The connection belong- 
ing-to-each-other, and the dependence, ought to be reciprocal, 
and give no criterion to decide what attributes are essential 
among those which belong to each other. 

Schelling’s Nature-Philosophy, while it seeks to blend the 
Platonic doctrine of ideas (modified in the Aristotelian sense) 
with Spinoza’s doctrine of substance, finds the real antitype of 
the notion in the ideas, the creative types, or characters of 
genera, the media between the unity of substance and the end- 
less number of individual existences. 

Hegel does not seek a real antitype of the notion, but holds 
that the notion is as much the fundamental form of objective 
reality as of subjective thought. He defines the notion to he 
the higher unity and truth of being and essence, to be the sub- 
stantial power existing for itself, and therefore the freedom 
and truth of the substance? But the notion as a form of 
human thought is not sufficiently characterised by this. 

According to Ulrici3 the logical notion is universality as 


1 Philosophy of Art, p. 51, translated into English, 1867. 
2 Logik, ii. 5 ff. in the ed. of 1834 ; Encycl. § 158 ff. 


3 Log. p- 452. 








150 § 56. Definition of the Notion. 


the category of separative thinking. But the mere category of 
universality will not sufficiently distinguish the notion from 
the general conception. 

Schleiermacher distinguishes the sensible and intellectual 
sides of the notion. The former is the Schema,' or common 
picture, i.e. sense-picture of the individual object represented 
confusedly, and therefore become a general picture from which 
several particular pictures, co-ordinate to each other, could 
quite wellarise. With respect to the intellectual side, Schleier- 
macher recognises? in the system of notions, that creation of 
the thinking reason, or of the ‘intellectual function,’ to which 
the system of ‘ substantial forms’ corresponds in real existence, 
or of powers and phenomena, in opposition to the system of 


judgments as the correlate of the system of ‘actions.’ This 


definition of Schleiermacher’s, when it places the notion as 
a form of knowledge in relation to a form of existence, is the 
right mean between the mutually opposed one-sided views of 
the subjectively-formal and the metaphysical Logics. It labours 
under the defect that it does not distinguish sharply enough 
between substance meaning existence, thing, ens, and substance 
meaning essence, essentiality, essentia. This seems to be a 
consequence of the’ Aristotelian vagueness in the use of the word 
οὐσία. Every conception of a thing is not a notion, nor does 
every notion rest upon a thing. The conception is a notion 
when the essential is represented in it, whether it be of a thing, 
an action, a property, or a relation.? Schleiermacher makes 
the opposition of the higher and lower notion parallel with the 
opposition of power and phenomenon, or universal thing (Genus 
and Species), and individual existence; so that (e. g.) the power 
of sight of the eye is to be thought of, in analogous relation to 
the single eye as a phenomenon of this power, as the universal 
notion of the eye is to the individual notion of the single eye. 
This theory has its root in the Aristotelian doctrine of the 


active power (ἐντελέχεια) as the essence,—1) ὄψις οὐσία ὀφθαλμοῦ 
ἡ κατὰ τὸν λόγον." 


| Dial. §§ 110 ff., 260 ff. 2 Ibid. § 175 ff. 
3 Schleiermacher himself partly recognises this, Dial. pp. 197, 
540, 545. 4 Arist. de Anima, ii. 1. 


The Essence. [51 








Beneke! considers the notion or general conception to be a 
form of “ analytical thinking.’ He incorrectly believes seasons 
correspondence with the essence as the ‘synthetical form ἡ 1s 

cidental. 

ἜΣ": definition of the notion corresponds with Schleier- 
macher’s :2—‘ the form of thinking, which represents the en- 
during basis of the phenomenon “i the existence which is re- 
presented in the notion is an enduring one, but one which can 
show itself in changing activities, now im one way; now in 
another—such an existence we call a living thing or a sub- 
stance ;* ‘ when the understanding strives to think the in- 
dividual thing as the lasting foundation of many phenomena 
(or, according to p. 5, as substance), its thought must take a 
form in which the meaning of many phenomena is compre- 
hended or conceived—every such thought we call a notion, 
and when it comprehends this meaning in the thought of an 
individual, an individual notion ;’° ‘the general notion re- 
presents the totality of the particular essences with their 
activities.’ 

Trendelenburg® understands by the notion, the forms . 
thinking which correspond to the real substance as ıts menta 
oe similar way Lotze™ calls a notion, that content which 
is thought of not merely as the conception in the mutually 
inter-dependent totality of its parts, but whose multiplicity 1s 
referred to alogical substance, which brings to ıt the method of 
combining its attributes. But the reference to a substance 
belongs to every substantive conception, and is not the pred 
guishing character of the notion. It cannot be grants t Ἢ 
Logic has nothing to do with the essential ; not, ἃ 
least, from the stand-point of Logic as the doctrine of know- 


ledge. 
Miles doctrine of the essence cannot be wholly summed up by 


i. 25 d. p. 50. 
1 System der Log. i. 255 ff. 2 Log. 2nd ed. p un 
7 Ibid. p- 56. 4 Syst. der Logik und Metaphysik, ii. 13. 
5 Ibid. p. 297. 6 Log. Unters. ii. §§ 14, 15. 
7 Log. p. 177 ff. § As Lotze thinks, Log. p- 82. 








152 3 57. Knowledge of the Essential, ete. 





saying that objects have the same essence, or are to be sub- 
sumed under the same notion, which have similar properties, or 
are most naturally related to each other. He knows that the 
further question arises—What objects are naturally related 
and so serve as the basis of the formation of a notion? aa 
would say that this latter question cannot be answered in a 
sentence, but is the one question of Inductive Logic. It is the 
business of induction to find out methods for discovering and 
testing the relations of properties, and so finding out whether 
they are 80 related that they can form the bases of notions. 
The inductive methods show what properties are essential. 
The portions of Mr. Mill’s Logic which refer to this question 
in debate are the most instructive in the whole book; cf. 
especially, vol. 1. pp. 131-170, and vol. ii. pp. 189-201, p. 216 ff, 
ΡΡ. 262-285. Essentiality, however, 4065 not depend upon ἑκὰς. 
tive Methods; Inductive Methods depend upon Essentiality ; 
and thus Mr. Mill fails to solve the problem of Essence. | = 


$ 57. We recognise and distinguish the essential— 

(a) In ourselves, immediately by feeling and medi- 
ately by ideas. Feeling is the immediate conscious- 
ness of the relation of our activities and conditions to 
the present existence and development of our whole 
life, of its single sides and organs, or of the life of other 
beings related to us. What aids is felt with pleasure ; 
what hinders, with uneasiness and pain. In the othisal 
feelings, more especially, the gradation of the worth of 
different developments reveals itself, according as they 
are sensible or mental, more passive or active, isolated 
or connected, limited to the individual or extended 
to a wider community, or consist in that relation on 
which the law of human will and action rests. The 
ethical ideas are developed (by abstraction) out of 
feelings. The knowledge of our own essence depends 


The ἃ Priori and ἃ Posteriori Elements, etc. 153 


























both on the consciousness of the ethical ideas, and on 
the amount of our actual existence in them. 

(b) By means of the knowledge of the essence in 
ourselves we recognise the essence of persons beyond 
us, more or less adequately, in proportion to their rela- 
tionship with ourselves. The relation between the 
knowledge of ourselves and of others is a reciprocal 
one. The clearness and depth of the knowledge of 
our own essence depend upon intercourse with others, 
upon living in connection with the whole mental de- 
velopment of the human race (just as one can say in 
theology, that the understanding of the revelation of 
God within us depends as much on the understanding 
of the historical revelation, as this does upon that). 

(c) The essence or the inner purpose of nature in 
animals and plants is the analogue of the ethical duty of 
man, and is to be known in the proportion of this analogy. 
The analogy is limited but not destroyed by a threefold 
opposition :—that the powers of the impersonal essence 
are of a very different and lower kind; that they do not 
strive to win to their end by means of a free conscious 
activity, but by unconscious necessity actually realise 
the tendency indwelling in them; and that the signi- 

ficance of their existence as ends in themselves is out- 
weighed by the significance of their existence for others. 

(d) With the inorganic objects of nature, existence 
as an end in itself, and self-determination, come after 
existence as a mean for another, and the mechanically 
becoming determined by another. Hence the possibility 
of knowing their inner essence is thrown into the back- 
ground by the knowledge of their outward relations. 








EEE EEE EEE Bra SEE -.-- - - - 
—— = zum ne Ν 
"- ν u - γι 
- -« a -“ «ὦ 


o> 











154 § 57. Knowledge of the Essential, etc. 





| (e) The essence of what exists not in the form of 
u existence or substantiality, and of what 
nas onl iti 
ay y a factitious independence, the result of art, 
is known partly according to its analogy with the 
life of . - wanes . + . . . A 
= independently-existing individuals, partly and 
ee aa nn 
y according to the significance which belongs to ıt 
as a mean to something else. 
Material truth is to be reached in our notional know- 
ledge of the_ essenti 
g „essential from the same g 
undergoes the same limitati d rei = 
g mitations and gradations, as in 


the case of perception ($$ 41-42) and of the indi- 
vidual conception ($ 46). 


The essential relation of the activity ofknowledge to the whole 
of the mental and ethical life depends upon ri 

The question whether human notions are present ἃ priori (if 
the phrase, according to Kant’s use, is applied to what is de- 
rived from the subject as such) in the mind (Geist) as innate 
possessions, or are raised up in it & posteriori by means of the 
senses, by way of gradual development, may be decided in the 
following way. Every notion contains an ‘a priori’ element 
not only in the sense in which this is true of every connie 
but, more particularly, because the knowledge of the essential “ 
things can only be reached by means of a knowledge of the 
essential in us (though this knowledge is often not develo ed 
into full consciousness). Schleiermacher' rightly places ‘iia 
development of the whole system of notions in relation to our 
self-consciousness. Man, as the microcosm, has in himself all 
the degrees of life, and thereon constructs his conceptions of 
outward existences. In this sense it may be rightly said that 
the system of all notions is originally contained in the reason 
or ‘intellectual function ;’ only we must not make the mistake 
of supposing that the actual system of human notions is inde- 
pendent of the objective reality and quite different from it. 


I Dial. $ 178. 


858. Class, Genus, Species, ete. 159 


When correctly constructed it represents the proper essence 


and arrangement of the objects. 
But the formation of any notion referring to the outer world 


᾿ς conditioned by the outer or ‘a posteriori’ factor just as much 
as by the subjective or «ἃ priori’ element; for if notional 
knowledge is to have truth, the completion of the contents of 
perception by analogues of our essence must conform to the 
phenomena, and can only be references of the outer phenomena 
of things to their inner essence. The a priori element is only 
ä priori as regards the outer world, and is by no means in- 


dependent of inner experience.’ 
It is impossible to admit the existence of notions, which, 


although unknown, may have been present as notions in us 
from the beginning. On any acceptation, this admission would 
contradict the course of human development. And the end 
which would induce us to make this unpsychological admission, 
the objective validity of notions apparently involved in it, is 
not satisfied by it. A pure subjectivism may connect itself with 


the presupposition of an a priori character; and, in fact, Kant’s 


critical philosophy has so connected itself. The truth lying at 
the bottom of this doctrine is,? that the human mind is able to 


reach a knowledge of objective reality. Cf. § 140. 


§ 58. Those individuals which have the same essen- 
tial properties make a class, or genus, in the universal 
sense. The genus is as much the real antitype of the 
extent as the essence is of the content of the notion. 
The essence has different degrees, and different circum- 
scribing groups of marks can serve as the basis of deter- 
mining the formation of the notion. In a similar way 
several classes or genera encircling each other can be 


distinguished, which are denoted successively by the 


1 Cf. Schleiermacher’s Ethik, ed. by A. Twesten, § 46, p. 59. 
2 As J. Hoppe has rightly remarked in his Gesammte Logik, i. § 54, 


p. 45, Paderborn, 1868. 














156 \ 58. Class, Genus, Species, ett.— 





terms, Kingdom (regnum), Sphere (orbis), Class (classis), 
Order (ordo), Family (familia), Genus (genus), Specids 
(species). Group (cohors) is sometimes inserted be- 
tween Kingdom and Sphere; Tribe (tribus) between 
Family and Genus ; Subdivision (sectio) between Genus 
and Species, and in other places; and Subspecies and 
Variety (varietas) between the Species and Individual. 
The notion of Race is specially applied, in definite 
cases only, to the most general division of men in 
natural history. It might be referred to Subspecies. 
The opposition of Genus and Species is frequently used 
to denote the relation of any higher class to any lower 
which is proximately subsumed under it without aes 
intervening members. 

Objects are generically different when they belong 
to different genera; specifically different when they bi 
long to different species of the same genus. They are 
gradually different when they differ only according to 
quantity or intensity. They are numerically ἀὐδέονυαὶ 
when they, although wholly similar in essence, are not 
identical, but are several objects. 


The characteristic of the species in natural history, main- 
tained by earlier investigators, was continuous fruitful pro- 
creation. Later research has made this criterion a relative one 
But this characteristic, so far as it holds good, is to be loka 
at only as consecutively, not as constitutively essential; for the 
possibility or impossibility of continuous fruitful procreation 
must depend upon the whole character of the organisation 
The true characteristic attribute of the species is πο Zoe 
tion, but the type. By type is to be understood, neither the 
mere outer form and figure, nor the peculiarity of any one 
given standard form, but the whole character of the organisa- 
tion—the Platonic idea, not in its historical but in its true 


their Reality and their Knowability. 


157 








— 


sense, the Aristotelian form, the Kantian ‘ Urbild der Erzeu- 
gungen,’! or? ‘the image which is afterwards realised.’ The 
possibility of reproduction only serves as a mean to recognise 
the correspondence in the type. Formations belong to a kind, 
if they, so far as their like stages of development are compared 
with each other, show correspondence in all essential attributes. 
Comparison is the function of the knowing subject only; 
essentiality of the marks compared is the objective moment 
which gives real meaning to the notion of species. Individuals 
which have been correctly arranged under a species (or any 
class) must agree with each other, not only in those marks 
which make up the content of the notion, but also in many 
secret relations. Hence it is seen that the notion of species 
(and every notion of class founded upon essentiality) is based 
upon the objective reality itself. George Henry Lewes* says, 
‘What is the aim of a zoological classification? [8 it not to 
group the animals in such a manner, that every class and genus 
may tell us the degree of com plexity attained by its organisation, 
so that the outer form may explain the inner structure ?’ But 
the degree of complexity on its part tells us the degree attained 
by every object in the scale of perfection. Cf. § 63. 

It is an inconsequence to recognise the real existence of 
the individual and then to deny the reality of species; and it 
would be an inconsequence to recognise the natural reality 
of species, and then to deny the natural reality of genus, 
family, and other wider divisions in which the narrower are in- 
cluded. For the reality of species depends upon the reality of 
essentiality. Certain elements must be recognised, not only to 
be eminently useful as fulera for the determination of notions, , 
but as eminently important and decisive for determining the 
existence and significance of real objects. If this be once 
allowed, the recognition of the graduation of essentiality, and 
with it the recognition of the reality of the graduated division of 


1 Krit. der Urtheilskraft. 
2 According to Spring, Ueber Gattung, Art und Abart. 
3 Aristotle : a Chapter from the History of Science, &c., p. 277, ὃ 323, 


1864 


ner χὰ σοῦ 


ee 














158 § 58. Class, Genus, Species, ete. 





external existence, cannot be well denied. Braun says rightly! 
—‘ As the individual appears to be a member of the species, 
so the species appears to be a member of the genus, the genus 
to be a member of the family, order, class, and kingdom.’ The 
recognition of the organism of nature and its regular division, 
as objective facts witnessed to by nature herself, is an essential 
requisite for placing natural history in a higher position.? 
Aristotle made species and genera δεύτεραι οὐσίαι, just as in- 
dividuals were οὐσίαι in the fullest sense of the word,? and 
so recognised them to be real. He saw in the natural classes 
a graduated series of ascending perfection. Linneus rightly 
believed the classes and orders of artificial systems to be a 
make-shift for the natural until they are known, but considered 
the true species and genera, when known, to be objective 
works of nature.‘ The knowledge of natural genera, families, 
and orders is always more uncertain than that of the species. 
The acceptation of an objective validity of natural division 
does not exclude the recognition of a certain relativity in the 
notion of species; as little as the objective existence of the in- 
dividual excludes the partial indefiniteness of the limits of 
the individual. In a genetic view of nature (such as the 
Darwinian,° whose fundamental thought Kant had already 
expressed hypothetically in his Kritik der Urtheilskraft), 
which is founded on the supposition of a gradual origin and 
partial transformation of species, the objectivity of the species 
for the world as it now exists can still be accepted. Fora 
realised tendency of nature to construct definite forms may be 
recognised, and objectivity does not mean absolute stability. On 
the basis of the Darwinian theory of species, inasmuch as its 
notion is referred to organisms existing contemporaneously 
at any given time, an objective validity in the full sense of 
the word can always be vindicated, because the systematic 
table of the classes of organisms rests on their genealogy, and 


Verjüngung in der Natur, p. 343. 
Cf. Rosenkranz, Logik, ii. 48 ff. 
Philos. Botan. § 161 sqq. 
Charles Darwin, On the Origin of Species, Lond. 1859. 


3 Cat. v. 


§ 59. The Individual Notion. 159 








so unites the genetic point of view of common origin with the 
teleological point of view.’ ‘ The difficulty of natural-history 
treatment does not now lie in the determination of the species, 
but in this, that every systematic category 1s considered to be 
a natural unity which represents the starting-point of a great 
historically developing movement. The genus and the higher 
notions (as much as the species) are not abstractions but con- 
crete things, complexes of connected forms which havea common 
origin.’? ΑΒ it is in the province of natural history, so is it in 
that of ethics. We must seek out the essential in the group- 
ing of the relations presented, and consequently in the forma- 
tion of the notion, which is thus not left to the subjective 
arbitrary choice, but is connected with objective law. The 
distinction of wider and narrower spheres rests throughout on 


the gradations of essentiality. 


§ 59. In those cases where individuals which belong 
to the same species are separated from each other by 
essential peculiarities, they form INDIVIDUAL NOTIONS. 
The individual notion is that individual conception, 
whose content contains in itself the whole of the essen- 
tial properties or attributes, common and proper, of 
an individual. A certain universality belongs to an 
individual notion also, inasmuch as it contains under 
it the different stages of the development of the indi- 
vidual. The conception of an individual living in time 
is not purely individual, unless it represents the indi-, 


vidual in a single moment of its existence. 


The schoolmen’s question about the ‘ principium individu- 


ationis, formed by the opposition of Aristotelianism and 


1 Cf, for the logical treatment, Trendelenburg, Log. Unters. 2nd ed. 


ii. 225 ff, 3rd ed. ii. 248 ff.; cf. ii. 78 ff. | 
2 Carl Nägeli, Entstehung und Begrif der naturhist. Art, 2nd ed., 


München, 1865, p. 34. 











mr teppei tiers ~~ 


160 § 60. Definition. Its Elements— 





Platonism,' rests on the presupposition that the universal is 
not only a notional, but also a real prius of the individual. 
It loses significance, whenever it is seen, that to descend 
from the general to the particular can only be done by the 
thinking subject; and that, in objective reality, the essence 
cannot exist before the individual in any such way that 
the individual must form itself upon it. The Nominalists 
(who went too far on the other side) have recognised this 
when they explain that what exists is, as such, an individual. 
After them Leibniz and Wolff explain that to be individual 
which is determined on all sides (res omnimodo determinata, 
or ita determinata, ut ab aliis omnibus distingui possit), and 
assert that the universal, as such, exists only in abstraction. 
Individuality is constituted not by one determination (such as 
Matter, Space, Time), but by the sum total of all. This does not 
prevent the distinction of essential and unessential, and of de- 
grees of essentiality, from existing in the objective reality itself. 

So far as properties, which belong to this or that individual, 
have essential significance, there are individual notions. From 
§ 46, it follows that individual notions are chiefly formed from 
the highest essences under the personal. 


$ 60. The DEFINITION or determination of the notion 
(Definitio, ὁρισμός) is the complete and orderly state- 
ment of its content ($ 50). All the essential elements 
of the content of the notion, or all the essential proper- 
ties of the objects (ᾧ 49) of the notion, must be stated 
in the definition. It is the expression of the essence 
of the objects of the notion. The essential elements 
of content are, partly those shared by the notion 
to be defined along with co-ordinate notions and so 
form the content of the superordinate notion, and partly 
those by which the notion is distinguished from the co- 
ordinate and superordinate notions. But since (§ 58) 

I Cf. Arist. Metaph. i. 6. 


the Notion of Genus and Specific Difference. ‘161 





the opposition of genus to species serves to indicate, 
generally, the opposition of any higher class to any lower, 
in so far as the latter is immediately subordinated to 
the former, the essential elements of the content of the 
notion to be defined can be separated into generic and 
specific. On this rests the postulate—that the definition 
contain the superordinate or genus-notion and the specific 
difference or what makes the species distinct. The state- 
ment of the genus-notion serves also to determine the 


form or category of the notion to be defined (whether it 


be substantive or adjectival, &c.). Simple notions, in 
which the totality of attributes is reduced to one attri- 
bute only, cannot have a regular definition (cf. § 62). 


Plato finds in Definition (ὁρίζεσθαι) and in Division (διαιρεῖν, 
κατ᾽ εἴδη διατέμνειν) the two chief moments of Dialectic,' but 
does not develope its theory more thoroughly. He does not 
expressly say that the Definition must contain the Genus and 
Specific Difference, but actually proceeds according to this 
axiom; e.g. in the Gorgias,’ in the definition of Rhetoric ; 
in the Republic, in the definition of the co-ordinate virtues 
(Wisdom, Courage, Temperance, and Justice) ; for he adds to 
the statement of their generic character the specific peculiari- 
ties. In the Dialogue Euthyphro, the ὅσιον is defined to be 
a μέρος of the δίκαιον, and then itis asked, ποῖον μέρος ? where- 
on Euthyphro answers— 10 περὶ τὴν τῶν θεῶν θεραπείαν. 
Socrates had already proceeded in this way, e.g. in the defini-- 
tion of the φθόνος ὃ as the λύπη ἐπὶ ταῖς τῶν φίλων εὐπραξί- 
ais. In the Platonic Dialogue Theaetetus,! the διαφορά or 
διαφορότης, or the σημεῖον ᾧ τῶν ἁπάντων διαφέρει 10 Epwrnder, 
is distinguished from the κοινόν, as when, e.g. the ἥλιον is 
said to be τὸ λαμπρότατον τῶν κατ᾽ οὐρανὸν ἰόντων περὶ γῆν. 
Plato combats the assertion, that a characteristic sufficient to 


ı Phaedr. p. 265 sqq. 2 Ibid. p. 462 ff. 
3 Xenophon’s Memorab. iu. 9, 8. 4 Theaet. pp. 208, 209. 


M 





——— 


- en en 
Br 9 τ΄ ande er nen - 
»»..- nalts Mer 




















162 


§ 60. Definition. Its Elements— 








distinguish science from mere (though correct) opinion is afforded 
by the consciousness of the διαφορά. In the Philebus' generic 
identity is distinguished from the διαφορότης of the uepn(species); 
the latter may be increased up to the most complete opposition. 
The remark that simple notions do not admit of definition is 
introduced and examined in the Theaetetus : *—dévvarov εἶναι 
ὁτιοῦν τῶν πρώτων ῥηθῆναι λόγῳ, οὐ γὰρ εἶναι αὐτῷ, ἀλλ᾽ ἢ 
ὀνομάζεσθαι μόνον, ὄνομα γὰρ μόνον ἔχειν " τὰ δὲ ἐκ τούτων ἤδη 
ξυγκείμενα ὥσπερ αὐτὰ πέπλεκται, οὕτω καὶ τὰ ὀνόματα at- 
τῶν ξυμπλακέντα λόγον γεγονέναι. In the Dialogue Politicus * 
the term διαφοραί signifies rather the species themselves, 
which are contained in the genus, and into which it can be 
divided, than the specific elements of content which must be 
added to the generic in the Definition of the species-notion. 
Definition is based on Division in the Dialogue Sophistes.‘ 
In the Platonic Leges® are distinguished—% οὐσία, τῆς οὐσίας 
ὁ λόγος, and τὸ övoua. By λόγος Plato here means both the 
notion and the definition of the notion, as, e.g. the λόγος of 
that which bears the name ἄρτιον is ἀριθμὸς διαιρούμενος εἰς ἴσα 
δύο μέρη. 


Aristotle teaches,® ὁρισμὸς οὐσίας τινὸς γνωρισμός "Ἶ ὁρισμός 
8 


a » 2 Δ i ΟΥ̓ λό 
EV @ apa un ἐνέσται AoYH 


> / \ 4: 7 , 
ἐστι λέγος τὸ τί ἦν εἶναι σημαίνων * 
Ὧν | , u. Φ e 4 m 1. 2 3 σι ἃ . 
αὐτό, λέγοντι αὐτό, οὗτος ὁ λόγος τοῦ Ti ἦν εἶναι ἑκάστῳ : 1.6. 
whatever expression does not contain the object (by its name), 
while it denotes it (in fact), is the assertion of the essence (or 

*,¢ . ς ε m 
the definition) of any thing °—o ὁρισμὸς ἐκ γένους καὶ διαφορῶν 
ἐστιν. ν 

The phrase Specific Difference (differentia specifica) is the 
translation (due to Boethius) of the Aristotelian διαφορὰ 
εἰδοποιός..0 Later logicians '' demand ‘ definitio fiat per genus 
proximum et differentiam specificam.’ It must also be pos- 


Pp. 12, 13. 2 P. 202. 3 P. 285. 
P. 219 sqq. * Ῥ 698, 6 Analyt. Post. ii. ὃ. 
Topic. vii. 5. 8 Metaph. vii. 4. 9 Top. i. 8. 
10 Ibid. vi. 6: πᾶσα yap εἰδοποιὸς διαφορὰ μετὰ τοῦ γένους εἶδος ποιεῖ. 
11 Founding on Arist. 70ρ. vi. 5, p. 143 a, 15, where μὴ ὑπερβαίνειν- 
τὰ γένη is demanded. 


the Notion of Genus and Specific Difference. 163 











tulated that what can be said in few words should not be 
expressed in many. But the postulate cannot be universally 
applied. For example, the definition which would subsume 
the circle under the proximate genus conic section, would in the 
majority of cases be less useful and convenient than that 
which subsumes it under the more general notion of plane 


figure, and in elementary geometry would be quite inadmis- 


sible. Cases of this kind may be generally reduced to the 
following formula:—The notion to be defined, A, falls under the 
proximate genus-notion B, and both under the proximate genus- 
notion c. A differs from B by the Specific Difference a; B 
from © by the Specific Difference 6. Now. it may happen that 
the two differences (a and 6) cannot be easily defined by them- 
selves, but easily coalesce into one whole difference a’, in 
which both are implicitly contained. When this happens, the 
Definition by a remoter genus-notion is easier and simpler 
than the Definition which contains the proximate genus-notion, 
and is therefore to be preferred, save in single cases where the 
purpose requires the more difficult definition. 

Modern Dogmatic Philosophy since Des Cartes lays great 
stress upon Definition; and Kant also, although he believed 
the knowledge of the essence of the thing to be unattainable, 
holds the stricter form of Definition to be important. Leibniz 
teaches that the genus and the difference making the species 
are ‘often interchangeable, for the difference may become the 
genus, and the genus the difference: this opinion, if, in 
accordance with Aristotle’s view, a real relation is represented 
in the reciprocal relation of the elements of content, must be 
limited to the case where several definitions are equally essen-- 
tial; as (e.g.), adulari can be as well defined to be mentiri lau- 
dando as laudare mentiendo, ut placeas laudato.' 

The Hegelian philosophy merges the Definition of the 
notion in its dialectical genesis. 


I Trendelenburg discusses the Element of Definition in the Leib- 
nizian Philosophy in the Monatsber. der Berl. Akad. d. Wiss. Juli 
1860, republished in his Hist. Beitr. zur Philos. iii. 48-62, Berl. 1867 ; 
cf. Log. Unters. 2nd ed. ii. 224 ff.; 3rd ed. 11. 247 ff. 


“2 





164 § 61. The Kinds of Definition. 





[ According to J. S. Mill, a Definition is a proposition declar- 
atory of the meaning of a word, and so must directly or indirectly 
include its whole content or connotation, or express the sum total 
of all the essential propositions which can be framed with that 
name for their subject. All names can be defined which have 
meaning. Even those whose meaning is summed up in a single 
abstract quality may be defined by their causes. Complete 
definition is not brief enough, and is, besides, too technical for 
common discourse. Hence arise incomplete definitions. Of 
these the most noteworthy is per genus et differentiam. Such 
definitions are useful abbreviations, but may be, and are con- 
tinually set aside in the progress of science." ] 


§ 61. DEFINITIONS are DIVIDED according to various 
points of view. We distinguish— 

1. Substantial and Genetic (Definitio substantialis 
and genetica sive causalis). The content of the notion 
to be defined is in the one case taken from the present 
existence, in the other from the origination of its 
object. 

2. Nominal and Real Definitions (definitio nominalis 
et realis). The former defines what is to be understood 
by an expression. The Real Definition has to do with 
the internal possibility of the object denoted by the 
notion, and thus with the real validity of the notion; 
for it either contains the proof of its real validity in the 
statement of the way in which the object originated, or 
was based upon such a proof. 

3. The Essential Definition and the Distinctive 
Explanation, or the Explanation ofthe Essence and 
Explanation by Derivative Determinations (Definitio 
essentialis; Definitio attributiva vel accidentalis sive 


[ Cf. Logie, i. 150-178. ] 


61. The Kinds of Definition. 165 





declaratio distinguens). The one gives the constitu- 
tively essential marks; the other the secondary, and 
consequently the attributes or different possible modes, 
but in the number and connection in which they belong 
exclusively to all the objects falling under the notion 
to be defined, and therefore sufficient to distinguish 
these objects from all others. 

4, Analytically-formed and Synthetically-formed Defi- 
nitions (Definitio analytica and synthetica). The one 
is formed in conformity with the existing use of speech, 
or according to the way of conception at present in use 
among the sciences; the other is formed anew and 
freely, independent of any demand of agreement with 
present use and want. 

5. Description (descriptio), Exposition (expositio), 
and Explication (explicatio) are less strict forms of 
explaining what belongs to the content of a notion, and 
so are related to Definition. These forms, along with 
Definition, may all be comprehended under the wider 
word Explanation (declaratio). Illustration (illustra- 
tio, exemplificatio), giving examples which are taken 
from the extent, is rather related to Division. 


There can only be one essence to the same object. Hence . 
it might be expected that there can only be one definition to 
the same notion. Different definitions of the same notion are 
possible in as far as a reciprocal dependence of the constitu- 
tively and consecutively essential attributes exists; so that, 
when any one or any group of them is stated, the sum total of 
the others cannot be separated from it. For example, we 
might define the circle by the curve of the straight line 
which produces it, or by the equidistance of every point of 
the circumference from the centre, or by the section parallel to 





166 § 61. The Kinds of Definition. 





the base of the right cone, or by the formulae of analytical 
ceometry ready to our hand; each of these attributes is 
so necessarily linked to the rest by mathematical laws, that 
the defined notion (of the circle) is the same in each. It 
is none the less undeniable, however, that only one definition 
fulfills the task of the definition in the fullest sense, viz. 
the definitio essentialis. Johannes Scotus (Erigena) said cor- 
rectly :! quamvis multae definitionum species quibusdam esse 
videantur, sola ac vere ipsa dicenda est definitio, quae a 
Graecis οὐσιώδης, a nostris vero essentialis vocari consuevit.— 
Sola οὐσιώδης id solum recipit ad definiendum, quod perfec- 
tionem naturae, quam definit, complet ac perficit. 

From the definitions given above several axioms may be 
derived about the relation which exists between the members 
of those different divisions. The substantial definition, at 
least when it stands alone by itself, is generally a nominal 
definition; the genetic, unless where the pretended genesis is 
impossible, is always a real definition, The nominal definition 
seems to be related to the accidental, or to the distinctive 
explanation ; and the real definition to the essential. But it is 
by no means the case that every nominal definition is merely 
an accidental definition, A nominal definition may be an 
essential, and an essential a nominal. When, e.g. Wolff 
defines truth to be the agreement of thought with the exist- 
ence which is thought, he himself correctly explains this defi- 
nition to be nominal, because it does not show the possibility 
of such a correspondence, and consequently does not warrant 
the real validity of the defined notion. Yet it is the essential 
definition of truth because it states its essence or fundamen- 
tally essential character. (If the essence were the ground of 
the thing, as some define it, every essential definition would 
at the same time be a genetic, and consequently also a real, 
definition ; but the essence is, only the ground of the other 
attributes of the thing, not the ground of the thing because 
it is not the ground of itself.) Every real definition is not at 
the same time an essential definition. It may also be an 


I De Divis. Nat. 1. 48. 


§ 61. The Kinds of Definition. | 167 





accidental definition, and an accidental may be a real definition. 
(The possibility of the thing may be warranted in a more 
external way, perhaps, by reference to some genesis which does 
not follow from the essence itself: in this case we have a real 
definition which is not an essential definition.) The division 
of definitions into analytically- and synthetically-constructed 
definitions has no definite relation to the other divisions. 

The terms Nominal and Real Definition are not thoroughly 
expressive ; for every definition defines not the name, nor 
the thing, but the notion, and with it the name and the thing 
so far as this is possible. But so long as the real validity of 
the defined notion is not warranted, it is always possible that 
a notion may have been defined which is only apparently 
valid, and is in truth only a mere name ora feigned notion 
corresponding to nothing real. On the other hand, the defini- 
tion of an objectively-valid notion serves at the same time to 
give a knowledge of the thing denoted by the notion. Con- 
sidered in this sense these terms justify themselves. 

Some logicians distinguish from the Real and N ominal Defi- 
nition a third kind, the Verbal Definition or explanation of 
words, by which they mean the mere statement of the meaning 
of terms. This co-ordination of the so-called verbal definition 
with the other kinds is inadmissible. In the statement of the 
meaning of a word it is the object of the explanation, not the 
hind of explanation which is peculiar. The so-called verbal 
definition, if it be a definition at all, is either the Nominal or 
Real Definition of the notion of a word. 

Definitions formed synthetically are only admissible where 
science actually requires new notions. The intermixture of 
determinations, which are admitted into a synthetic definition 
of a notion according to the individual judgment, with the 
elements of the content of that notion, which, according to the 
universal use of language, bears the same name, has always 
been one of the most inexhaustible sources of errors and mis- 
takes. Many of Spinoza’s definitions serve as examples—his 
definition of Substance, for instance, of Love, &c.; and not 
a few of Kant’s, of knowledge ἃ priori for instance, and of 





168 § 61. Zhe Kinds of Definition. 





the Idea, of Freedom; the moral definitions of faith also, in 
their relation to its actual reference, which is also conformable 
to the use of language, to the acceptance as true of distinct 
propositions ; or, reciprocally, the definitions enunciated in this 
last sense, in their relation to another use of the word, in 
the sense of trust in God and Men, &c.' (The terms syn- 
thetic and analytic definition, introduced by Kant, are parti- 
cularly useful to point out the distinct kind of quaternio ter- 
minorum, which rests on the confusion mentioned above. On 
the other hand, one must remember that the distinction 
denoted does not so much concern the character of the 
definition itself as the kind of its origin in the subject. It is 
rather a psychological than a logical distinction.) 

Aristotle teaches: ὁ ὁριζόμενος δείκνυσιν ἢ τί ἐστιν ἢ τί σημαί- 
ve. τοὔνομα He calls the latter kind of Definition λόγος 
ovouarwöns, the former is called by Aristotelians ὅρος πραγ- 
ματώδης (realis) or ὅρος οὐσιώϑδης (essentialis). _ We can also 
give a definition of notions which have no real validity, as, for 
example, τραγέλαφος. But we can only know the essence or the 
τί ἐστὶ of what is, and of which we know that itis. Hence, 
e.g. we cannot know the essence of τραγέλαφος, ti δ᾽ ἐστὶ τρα- 
γέλαφος, ἀδύνατον εἰδέναι Knowledge advances from exist- 
ence to essence and reason—éyovtes ὅτι ἔστι, ζητοῦμεν διὰ τί 
ἐστιν. The full knowledge of the τί ἐστι includes the know- 
ledge of the διὰ τί ἐστιν, and is distinct from it, only in a 
formal relation. In other words, the knowledge of the essence 
of the thing must found itself on the knowledge of its origin. 
The essential explanation must either include the cause of the 
object along with the genetic demonstration, or must presup- 
pose the knowledge of the cause along with the conclusion of 
the demonstration. This postulate falls to the ground only in 
the definition of causeless self-evident principles.2 The Aris- 
totelian notion of the essential explanation, or ὁρισμὸς τὸ τί 
ἐστι σημαίνων, unites in itself these two moments—the state- 


1 Cf. § 160. 2 Anal. Poster. ii. 7. 
3 Ibid. ii. 10. 4 Ibid. ii. 7. 5 Tbid. ἐν 10. 


61. The Kinds of Definition. 169 





ment of the essential attributes, and the proved reality of the 
object. 

Leibniz distinguishes ‘ Definitiones nominales, quae notas 
tantum rei ab aliis discernendae continent, et reales, ex quibus 
constat rem esse possibilem.’! He thus, on the one hand, includes 
in the notion of definitio realis a moment less than Aristotle does 
in the corresponding notion of ὁρισμὸς τὸ τί ἐστι σημαίνων. He 
does not expressly demand a statement of the essential marks(for 
the essence is not identical with that by which the possibility 
and the genesis of the object is known). On the other hand, 
he includes a moment more than Aristotle does. He does not 
admit, as Aristotle does, that the real definition contains either 
the proof of the reality and of the genesis of the notion, or 
founds itself on a previous demonstration. He only asserts 
that it gives the proof of the internal possibility. 

Starting from these definitions of Leibniz, Wolff distin- 
guished more strictly the two elements which lay combined in 
the Aristotelian notion of ὁρισμὸς τοῦ τί ἐστι, and separated 
the simple Aristotelian opposition into the double one of, on 
the one side, the definitio nominalis and realis; and, on the 
other, of definitio accidentalis and essentialis. He says :— 
‘definitio, per quam patet rem definitam esse possibilem, 
realis vocatur:? definitionem essentialem appello, in qua enu- 
merantur essentialia, per quae definitum determinatur ; acci- 
dentalem dico, in qua enumerantur vel attributa, vel quae per 
modum attributorum insunt, modorum ac relationum possibili- 
tates, quibus definitum determinatur.”? 

Kant, on the other hand, recombined the two moments. In 
his explanation of nominal and real definitions, he includes the 
characteristics of accidental and essential definitions.‘ 

The post-Kantian logicians have partly followed Wolff or 


1 Acta Erudit. p: 540, 1684. 2 Log. § 191. 

3 Log. ὃ 192. The older logicians distinguished after Boéthius the 
definitio secundum substantiam, que proprie definitio dicitur and the 
definitio secundum accidens, quae descriptio nominatur. Cf. Abélard, 
Dial., in Cousin, Oeuvr. ined. d’Ab. § 493; Joh. Scotus, as above. 

4 Log. ed. by Jiische, § 106. 














170 st. Fhe“Kinds of Definition. 


“ 


.-..... .... -- ς- - + 








Kant,! and have partly? referred the distinction of nominal 
and real definition to that distinction which Wolff expressed 
by the terms accidental and essential definition? This termi- 
nology is, however, not advisable, partly because the mean- 
ing of the words used refers more to the distinction between 
the subjectively arbitrary, and objectively or really valid, 
determination of the notion, than to the non-essential and essen- 
tial attributes; and partly and chiefly because it is foreign to 
prevailing use and wont in mathematics and other sciences.‘ 
Those mathematical definitions, e.g. which are brought forward 
by Euclid to prove the construction of required figures, 
whether they contain constitutively essential or secondary attri- 
butes, are to be called Nominal definitions ; but definitions 
which contain only secondary determinations, as, e.g. that of 
the straight line, as the shortest distance between two points 
(since the essence of straightness is rather continuous direc- 
tion), although it may prove its objective validity, are to be 
called Accidental or Attributive Definitions, or Distinctive 


1 Herbart, Lehrb. zur Einl. in die Philos. $ 42, following Wolff and 
Aristotle, finds the characteristic attribute of the real definition in the 
validity of the notion. 

2 Schleiermacher, Dial. § 266; and Drobisch, Log. 2nd ed. § 109. 

3 In the 3rd ed. of his Logic, in §§ 115, 116, which correspond to 
§§ 109, 110 of the 2nd ed., Drobisch uses the expressions, ‘ distinctive 
explanation’ and ‘definition,’ in the sense of accidental and essential 
definition ; and in § 120 introduces as the common use and meaning of 
the term real definition, which he means to disregard, that explanation 
by which the possibility, or more correctly the validity, of a notion is 
made clear. 

4 Drobisch has himself followed the use which he exclaims against 
in the 2nd ed. of his Logic, in his Empirische Psychologie, e.g. at 
p- 292, where he says of the prevailing explanations of the mental 
faculties, ‘they are only explanations of names which do not warrant 
the reality of their objects.’ A discrepancy between the terminology in 
Logic and in the other sciences is always a misfortune ; and should be 
the less admissible because it may be avoided without innovations, by 
a simple reference to definitions given by Wolff after Aristotle and 
Leibniz. 





61. The Kinds.of Definition. 171 








Explanations. When the penal code distinguishes felony 
and misdemeanour, and defines felony as “a crime punished 
by forfeiture either of the fee or of the goods and chattels of the 
criminal” this is an Attributive Explanation (Distinctive 
Explanation); but when ‘trial’ is defined to be the proving 
of the resolve to commit a felony or misdemeanour, by deeds 
which contain a beginning of the procedure in this felony or 
misdemeanour, this is an essential explanation. Both explana- 
tions are equivalent, so far as the distinction between Nominal 
and Real Definitions goes. | 

[J. S. Mill reduces all definitions to Nominal Definitions. 
No definition is intended to explain the nature of a thing. 
All definitions are of names, and of names only. In some 
definitions, however, it is clearly apparent that nothing is 
intended save to explain the meaning of a word; while in 
others, besides explaining the meaning of the word, it is in- 
tended to be implied that there exists a thing corresponding 
to the word. There is a real distinction between definitions of 
names and what are erroneously called definitions of things; 
but it is, that the latter, along with the meaning of a name, | 
covertly asserts a matter of fact. This covert assertion 15 not 
a definition, but a postulate. On this doctrine of definition 
Mr. Mill bases his hypothetical theory of demonstration, since 
the certainty of the so-called necessary sciences depends on 
the correctness of the hypothesis which connects their defi- 
nitions with real things. Definitions, however, are not arbi- 
trary, and though of names must be grounded on a knowledge 
of the corresponding things.! In this theory of Definition 
Mr. Mill seems to contradict the doctrine enforced with so 
much vigour when treating of propositions in general, that 
propositions express not a relation between two names, but 
between matters of fact. Had Mr. Mill only applied this 
same doctrine to that class of propositions called definitions, 
he would have hesitated ere he reduced all definitions to defi- 
nitions of names, and might have been led to a theory of 
demonstration more consistent with fact, than that which makes 


[' Cf Zögie, i. 160-178, ii. 216-220. 








172 δ 62. The most notable 





him say that there may be any number of sciences as necessary 


as geometry if only suitable nominal definitions are combined 
with a few real axioms. 


Mansel gives a very good resumé of Aristotle’s views upon 
Definition. He does not recognise Definition so far as it has 
to do with material truth or correctness, or so far as it gives 
information about the meaning of words we were previously 


ignorant of, Logical definition has to do only with the sub- 
jective distinctness of a notion.! 


Sir Wm. Hamilton gives the common division of definitions, 


but, refusing to introduce them into pure Logic, relegates the 
discussion to applied Logic.? 


Aug. De Morgan divides Definitions into nominal and real. 
Nominal definitions substitute for a name other terms, A 


real definition so explains a word that it suffices to separate 
the thing contained under that word from all others.?] 


$ 62. The most noteworthy FAuLTs of ΠΕΡΙΝΙΤΙΟΝΒ 
are :— 

(1) Too great width or narrowness (definitio latior, 
angustior suo definito). The definition is of greater 
or less extent than what is defined, and the rule is 
broken that the definition be adequate (definitio adae- 
quata), or that the definition and what is defined be 
reciprocal notions. 

(2) Redundancy (definitio abundans). Along with 
the fundamentally essential determinations are given 
derivative ones, which belong only ‘to the development 
of the notion. 

(3) Tautology (idem per idem). The definition ex- 
plicitly or implicitly repeats the notion to be defined. 

' Cf. his ed. of Aldrich’s Log. 4th ed., Appendix, pp. 181-197. 
2 Lect. ii. 22-36. 
ὁ Cf. Formal Logic ; or, the Calculus of Inference, p. 36, 1847.] 


Faults in Definition. 173 





i (4) The Circle or Dialellon (circulus sive orbis in 
definiendo). A is defined by 8, and B again by A; 


or A is defined by B, B by c, © by p, and D or any 
following member is again defined by a. This com- 


4 TER 7 
monly happens in consequence of an ὕστερον πρότερον, 
16. of an attempt to define a notion, whose pape 
<now those 
presuppositions are not known, by means of 


notions which already presuppose it. | 

(5) Definition by jigurative expression, by mere = 
tions, by co-ordinate and hora notions. Pr 
negative definition is legitimate with cose no : : 
and in simple notions their mere separation rom ᾿ 
state of confusedness among other notions, and ex- 
planation by means of the statement of their extent, 1s 


scientifically correct. 


The following definition of the infinitely little Sie 2 ” 
be found in a recent text-book on the Differentaal Er us) 
is an example of too great width :—* A quantity whic Ἢ = i 
think as a fraction, with the numerator always .. = 
same, but the denominator continually increasing, we a foal 
infinitely little.’ The definiens has here a wider exten . 
the definiendum, for the denominator steadily —— Ww ot 
it advances in the following way :—10, 15, 173 183 ea 
yet the fraction is not in this case infinitely little. = eo 
tation is needed—the series of fractions must also be of suc a 
kind that whatever number be given, one member of = series 
can always be found, which is smaller than its econ ue, ai 
stands nearer zero; in other words, the series must ave zero 
as its limit of value. Cato’s definition of an orator 18 too —_ 
__<Orator est vir bonus dicendi peritus ;’ for individuals can : 
thought of which belong to the extent of the ar a 
do not belong to the extent of the definiens. K. H. re : 
definition is also too narrow,—* Thought is that act of the in τ 
ligence, by which notion: an activity and a substance are per- 











174 362. The most notable 


ceived to be one (congruent) ;’ for it includes one kind of think- 
ing only. The definition, which is too narrow, is false as a 
proposition and as a general reference. The definition, which 
is too wide, is true as a proposition, but its converse is false. 
(In the converse the subject becomes predicate and the pre- 
dicate subject; cf. § 85—The Doctrine of Conversion.) An 
adequate definition is true conversely, for the definitum and 
the definiens must be reciprocal notions. Conversion can 
therefore serve as a means of testing definitions. 

Redundancy is exhibited in the explanation,— Parallels are 
lines which have the same direction, and always keep the same 
distance from each other. But there is only an apparent re- 
dundancy when, in the definition of the similarity of rectilineal 
plane triangles, the equality of the angles, as well as the propor- 
tionality of the sides, is taken into-consideration ; for though in 
the triangle one of these two conditions can be deduced from 
the other, the two, when united, express the full essence of simi- 
larity, since the general definition of similarity of rectilineal 
plane figures can be established only on the union of the two 
attributes. 

Tautology occurs in the answer given by Callicles to the ques- 
tion of Socrates : rivas λέγεις τοὺς βελτίους :---τοὺς ἀμείνους ἔγωγε, 
whereon Socrates replies: ὀνόματα λέγεις, δηλοῖς δ᾽ οὐδέν. The 
same fault occurs when living power is explained to be the 
inner ground of life. But no tautology occurs when, if a 
species-notion is to be defined which has no peculiar name, but 
is denoted by the addition of an adjective to the name of a 
genus, the name of the genus is repeated in the definition. 
This procedure is not confined to N ominal Definitions (as has 
sometimes been asserted); for if the species is to be defined, 
the genus in every case must belong to the notions already 
previously defined, and therefore to be presupposed as known. 
Thus, e.g. the definition—a straight line is a line with a 
direction constant in itself—is without fault as a real and 
essential definition; for the definition of a line (as a construc- 
tion formed by the motion of a point) must be presupposed, 
if the notion of the species straight line is to be defined. 


Faults in Definition. 


An Hysteron proteron is contained in the - es 
ize as the capability of increasing and diminis ning. cies 
ΜΝ a circle explanation; for increase 18 only addition 2 si : 
pt diminution is only taking away from size. > 5 
τὰ h I. G. E. Maass gives of pleasure’ is really acircle. . 4 
ee A feeling is pleasant when it is desired because 0 

oO 


anation of 


says: 


i j re in some way represent to be 
me | = aaa to be good which warrants 
eet ises pleasure, and affects us pleasantly ;—the ee 
μῆς aa pleasant feelings.” The NE Pe Ἢ A 

Ι xy the desire, and the desire again by “ ple 
ρα ar this circle is to be avoided, = ge > ei 
definition of feeling to the notion of futherance ; 


= oars 
forms its scientific presupposition, The feeling Kee ΓΝ 
i ss of the futherance of life. 
is the immediate consciousne gi POG 
j idea of the good the sur σ 
When Plato calls the 1 ee 
id not mean this figurative desig 
dom of ideas, he did no a gen 
iti ieved the good, as a simple g 
a definition ; for he believec g | 
: es n, to “ indefinable. But we cannot presuppose that > 
Ῥ' En had the same logical consciousness when nr 
c c : r 
defined things to be numbers, — Justice, nn 2, 
i I ὃς ἰσάκις ἴσος ; nor that Jaco 
x umber, ἀριθμὸς ἰσάκις woos; al 
ork = he “at —‘the new birth is the epi gE of 
d it w > > 
| ds heavenly essence in the centre of the animal er = 
(Heaven and earth, and all that 1s therein) is the body 
a d,’ &e Explanations, too, like the following—J mes 
0 ὃ ᾿ : ora 
a the ethical idea; the state ıs man writ ers > 
Church is the body of Christ; nn is the ın mn 
| i man ; 
justi taken up its abode in every 
court of justice, which has ge 
Ι in figuratively true thoughts, 
and such like—which contain hg vel} noe 
git the explanation of the parable in its peculiar sense, In 
iti > figurativeness in 
ientific definitions. The figura 
order to become scienti i urat ie 
Zeno’s definition of πάθος as the ἄλογος καὶ Tapa a ur 
κίνησις," where the meaning of * motion’ wavers between 
3 


i i id. p. 243. 
1 In his Versuch über die Gefühle, i. 39. 2 Ibid. p 


3 i . 244. a rt sr g j 3 
4 πρὶ T #. vii. 110: ef. Cie. Tuse. iv. 6: aversa a recta ratione 
iog. Laert. vil. 5. oes 


contra naturam animl commotio. 





176 ὃ 62. The most notable Faults in Definition. 


ing and desire, is more indirect, and therefore more injurious in 
Science. The same fault of indirect figurativeness injures 
Wundt’s explanation— Sensation is the inference which the 
mind draws from a series of signs lying in the nerve-processes.’ 
Under the figure of inference the difficulty is concealed, whether 
and how a sensation can be the result of motions, and what 
kind of connection does actually exist. 

Euclid’s definition— Parallel lines are straight lines in the 
same plane, which, produced infinitely, will never meet —cha- 
racterises parallel lines by a determination merely negative, 
and only derivative, not fundamentally essential. It leads to 
confusion, which does not occur in definitions formed upon the 
notion of direction (cf. § 110). The definition—epırrov (ἐστι) 
τὸ μονάδι μεῖζον aptiov—may be taken, with Aristotle, as an 
example of a faulty definition formed by means of co-ordinate 
notions. 

In formal reference it is always more correct to define co- 
ordinate notions by means of the genus-notion and their 
specific differences. For example, the even number is a num- 
ber which is divisible by 2 without remainder; the odd is a 
number which, divided by 2, has a remainder of 1. It would, 
however, amount to a formal rigorism, if one were wholly to 
despise the shortness and comprehensiveness which can be 
reached, in many cases, by reference to a foregoing definition 
of a co-ordinate notion; for example, after the definition of the 
even number has been granted, not to allow the definition,— 
the odd number is that which is distinguished from the even 
by unity. 

The enumeration of the members of the extent of a notion 
(e.g. the conic section is that mathematical figure which divides 
into these four forms—circle, ellipse, parabola, hyperbola) is 
useful to illustrate this notion, if it goes before or comes after 
definition. When it stands in the place of the latter, it be- 
comes the faulty definitio per divisionem or per disjuncta. 

Since simple notions, as has been already remarked (§ 60), 
admit of no proper definition, but can be brought into con- 
sciousness and distinctly distinguished from other notions only 


§ 63. Division. 7) he Ground of Division, etc. 17 





by abstraction and isolation, the highest scientific strictness 
possible in this case is reached by the form of the accidental 
definition. For example, the notion of the point is to be de- 
fined by a progressive series of limitations, which find scientific 
expression in the following accidental definitions— Space is what 
remains over from the sum total of sense-intuition, after the 
abstraction of matter (i.e. of what is unchanged in motion) ; ma- 
thematical body is a finite part of infinite space, or a limited 
space; surface is the limit of body, the line of surface, and the 
point of the line. After that the simplest element has been 
reached in this way, the other constructions can be genetically 
reconstructed from them, and defined by the explanation of the 


essence. 


$ 63. Division (divisio, διαίρεσις) is the complete 
and orderly statement of the parts of the extent of a 
notion, or the separation of the genus into its species, 
The species-notions are distinguished from the genus- 
notions by this, that the more indistinct features of the 
genus-notion, by the addition of the specific differences, 
have aciually taken the different forms or modifications 
of which they are capable. Hence, in the division of 
the genus-notion, the formation and arrangement of the 
species-notions must be founded on these modifications 
of the characteristics of the genus. Accordingly 
different divisions are produced, in any genus-notion, 
which unites in itself several characteristics able to be 
modified, when the species are distinguished according 
to the differentiations of the one or the other. That 
attribute of the genus, on whose modifications the 
formation and arrangement of the notions of species is 
based, is called the GROUND OF DIVISION or PRINCIPLE OF 


DIVISION (fundamentum sive principium divisionis) ; the 
N 





178 863. Division. The Ground of Division, ete. 








species-notions themselves, the MEMBERS OF Division 
(membra divisionis, less strictly membra dividentia). 
Division is Dichotomy, Trichotomy, Tetrachotomy, Poly- 
tomy, according to the number of the members in 
division. The formal postulates of Division are:— 
that the spheres of the members of division, taken 
together, exactly correspond to the sphere of the notion 
to be divided, and therefore fill it without hiatus ;— 
that they in no way overpass it; and,—that they do 
not cross but completely exclude each other. In the 
arrangement of the members of division, those which 
are the most closely related to each other should be 
placed together. Division determined by the modifi- 
cations of a single attribute is called artificial division. 
It has scientific value in the proportion in which the 
presupposition is true, that by means of some causal 
connection the modifications of this attribute are linked 
to the corresponding modifications of the whole essential 
attributes. The most perfect Division founds itself on 
the essential modifications of the essentially constitutive 


attributes. It depends on the essential definition of 


the notion to be divided. It is called Natural Division 
in the same sense as the system which results from a 
continuous series of such divisions is to be called a 
natural system. Divisions of this kind cannot be formed 
in any way according to an external uniform scheme. 
It is incorrect to look for an equal number of members 
of division in all cases in divisions of this kind so far 
as they correspond to the ideal demand. A strict 
Dichotomy may always be attained by means of a nega- 
tive species-notion ; but then it labours under the 


Dichotomy, Trichotomy, ete. 179 





defect that the species classed under the negation are 
left indefinite. When there are several of them the 
dichotomy will show itself to be illusive, as soon as they 
come to be specified according to their positive attributes. 
Such a division therefore can only serve as an introduc- 
tion in the formation and testing of divisions. Tri- 
chotomy usually finds application where a development 
occurs which is independent and rests on internal 
causes; because such a development is accomplished 
in the form of an opposition of two members and 
their fusion in a third. Mere trichotomy, however, 
not unfrequently falls short of the domain of actual 
existence; for actual existence in its higher grades does 
not usually advance in simple series. The higher unity 
to be brought about often results from a great number 
of cross oppositions. 


By the natural method of division Cuvier means (Régne 
animal, Introduction), ‘ An arrangement in which existences 
of the same kind will rather be neighbours of each other than 
of those of other kinds, kinds of the same order of each other 
than of those of other orders—and so on.’ Cuvier explains 
this to be the ideal which natural history must aim after ; for itis 
‘the exact and complete expression of the whole of nature.’ Cf. 
§ 58. 

The doctrine of Divisions, whose scientific value Plato had 
already recognised, formed with Aristotle an integral part of 
Analytic. Plato preferred Dichotomy. Every opposition has 
two members.! The parts must be species (εἴδη), 1.6. formed 
according to essential differences,2—xat apOpa, 7 πέφυκεν---εἰς 
ἐν καὶ ἐπὶ πολλὰ πεφυκότα ὁρᾶν.Σ In his later period Plato was 
fond of adding to the two members of the opposition, as a 
third, τὸ ἐξ ἀμφοῖν μικτόν. He did not, however, recognise in 


1 Prot. p. 332. 2 Phaedrus, 265. 3 Cf. Polit. 262 sqq. 


n 2 





180 § 63. Division. The Ground of Division, ete. 





this third member (as Hegel does) the highest but intermediate 
element.! In the dialogue Sophistes* dichotomy is traced back 
to the general point of view of ταὐτόν and ἕτερον T etracho- 
tomy results from the combination of two grounds of division. 
Aristotle treats of the doctrine of the grounds of division ın 
Top. vi. 6, and De Part. Anim. i. 3, where he more especially 
notices the passing from one ground of division to another. 
He explains‘ the advantages and disadvantages of dichotomy 
formed by negation. We do not find that he had the modern 
preference for a distinct number of positive members of divi- 
sion; this is, for the most part, a consequence from the 
Kantian doctrine of the Categories. Kant believes that he 
can, according to his table of categories, which contains com- 
pletely and systematically all the elementary notions of the 
understanding, determine ἃ priori every moment of every 
speculative science and their arrangement.® Hence the scheme 
of the categories has served kim, and still more his disciples, as 
a leading principle in the treatment and division of the varied 
scientific material. Goethe himself was once induced by 
Schiller to attempt the thankless task of dividing his doctrine 
of colours according to the Kantian Categories. One of the 
‘singular reflections’ which Kant attached to his table of 
‘ategories has proved very rich in consequences. He says 
that every other ἃ priori division of notions must be a dichotomy 
(a is partly B, partly not B); but a trinity of Categories 
appears in every class, and in each case the third arises from 
the union of the first and second. This remark of Kant’s has 
led to that scheme of thesis, antithesis, and synthesis, which, 
on all points, conditions the methodical course in Fichte’s con- 
structions, and still more in the Hegelian dialectic. These 
trichotomies are not purely arbitrary, but rest on a true insight 
into the essence of development. Yet they cannot be recog- 


ι See Phileb. 23; Tim. 35 a; cf. the author’s article in the Rhein. 
Mus. für Philologie, N. S. part ix. p. 64 ff., 1893. 

2 Pp, 253. 3 Cf. Polit. 287. 

4 Anal. Post. ii. 18: De Part. Anim. i. 2, ὃ. 

5 Krit. der r. Vern. § 11. 


Dichotomy, Trichotomy, etc. 181 








nised to be the only valid, and everywhere predominating, form 
of division; not merely because now and then the phenomena 
of nature fall behind the notion, as Hegel says, and because 
dialectic thought is not yet thoroughly the lord of things; but 
because the simple uniformity of trichotomy of itself is not 
enough to represent the fulness of the phenomena of natural 
and mental life. In many cases this fulness corresponds more 
to the intertwined double method of Schleiermacher’s te- 
trachotomy, which starts from two cross dichotomies. Schleier- 
macher endeavours to prove the unity which is above the 
double opposition. (For example, he divides the sciences into 
the speculative and empirical knowledge of reason, and the 
speculative and empirical knowledge of nature, or into ethics, 
science of history, physics, and natural science, according to the 
oppositions of reason and nature, force and phenomenon, and 
finds in Dialectic, which starts from their common principles, 
the vital point of unity.) But this fourfold or fivefold com- 
bination cannot be suitably applied to every matter, any more 
than the ninefold division of George, which combines the prin- 
ciples of Hegel’s and Schleiermacher’s methods of division, or 
other schemes published by others. The only general rule 
which can be established is,—every natural division must be 
conformable to its objects.’ 

The doctrine of Division owes to Herbart the remark, that, 
as the division of a notion depends upon the division of an 
attribute, which forms the ground of division, all divisions in 
the last resort return necessarily to certain fundamental divi- 
sions, in which only a single attribute of the notion to be 
divided is the ground of division; but this notion is itself the 
ground of division, and the series of species or individuals must 
therefore be given immediately. For example, the series of 
colours, sounds, numbers, &c.? ᾿ 


' Cf. Trendelenburg, Zog. Unters. 2nd ed. ii. 233; 3rd ed. ii. 256; 
cf. Johan. Scotus (Erigena) in Prantl, ii. 32, and Plato, Phaedr. p. 265. 

2 See Herbart, Lehrbuch zur Einleitung in die Phil. § 43; cf. Dro- 
bisch, Logik, 3rd ed. § 123. 





182 § 64. Subdivision and Co-ordinate Division. 

















§ 64. When the single members of division are again 
divided into their subspecies, Subdivision results. When 
one and the same notion is divided according to two 
principles, Co-division arises. The same ground of divi- 
sion, on which a co-division of the genus-notion rests, 
can generally serve as ἃ ground of division for the sub- 


division or partition of species into subspecies, under 
the limitations which result from the mutual relations 
of the dependence of the attributes.! Progressive divi- 
sion must proceed continuously by species and sub- 
species without hiatus (divisio fiat in membra proxima). 
It contradicts the laws of complete formal strictness if 
the subdivisions into which a co-ordinate species may 
be divided are placed directly beside the species, so that 
the subspecies may come in instead of whole species. 
It is a licence sometimes convenient however, in cases 
where the limit between the different ranks of species 
and subspecies is indistinct, and by no means to be 
rejected unconditionally, especially in ἃ widely ramified 
division of a very comprehensive material. Only do 
not let the possibility of survey be lost, nor the divi- 
sion, in this reference, fail in its design. 

For example, it would be an unjustifiable rigorism not to 
admit the division of natural objects into Minerals, Plants, and 
Animals (instead of, I. Inorganic objects or minerals; II. Or- 
ganic objects: 4. Plants; 5. Animals); more especially be- 
cause if the capacity of consciousness be the ground of the 
principal division, minerals and plants may be taken together 


as subspecies under the chief species—inanimate objects of 
nature, and animals alone make up the second chief species. 


In the case of simple co-ordination the gradual sequence of 


1 Cf, §§ 50, 54. 


§ 65. The most notable Faults in Division. 183 





internal value appears as a ground of division. When Epi- 
curus divides the desires in their ethical reference into three 
classes,—naturales et necessariae, naturales et non necesszriae, 
nec naturales nec necessariae—the gradatjon in the proportion 
of its correctness forms the ground of division which may 
justify this kind of co-ordination. In any case the fault of 
superfluity is not justifiable which Cicero! expresses against 
this division when he says, ‘ hoc est non dividere, sed frangere 
rem;—contemnit disserendi elegantiam, confuse loquitur.’ 
Cicero reproaches Epicurus with counting the species as a 
genus in this division (‘ vitiosum est enim in dividendo partem 
in genere numerare ’), and on his side only admits the divi- 
sion—I. Naturales: a. Necessarlae; ὦ. Non necessariae; 11. 
Inanes. In this last division the naturales necessariae and the 
naturales non necessariae are only species, and the inanes, on 
the other hand, a genus. But this is not the case from the 
Epicurean point of view, which really makes the three classes 
co-ordinate with each other. 

Division can only descend to such groups as are not essen- 
tially separated from each other. Subdivisions are not 
formed for the sake of very small differences. Seneca warns 
against the extravagances which the usages of rhetorical 
arrangement seem to have introduced into the rhetorical 
schools of the ancients, in the words—‘ quidquid in maius 
crevit, facilius agnoscitur, si discessit in partes; quas vero 
innumerabiles esse et minimas non oportet; idem enim vitil 
habet nimia, quod nulla divisio ; simile confuso est, quidquid 
usque in pulverem sectum est.’? Quintilian says the same 
of partitio: ‘ quum fecere mille particulas, in eandem incidunt 
obscuritatem, contra quam partitio inventa est.’ 


$ 65. The most important DEFECTS. in DIVISIONS 
are :— 

(1) Too great width or narrowness. (The latter occurs 
chiefly by overlooking transition-forms. ) 


ı De Fin. ii. c. ix. 2 Epist. Ixxxix. 








184 § 65. Zhe most notable Faults in Division. 





(2) The placing side by side species-notions, which 
do not purely exclude each other, whose spheres fall 
wholly or partly within each other. 

(3) The confusion of different principles of division. 
(This fault is often connected with the others.) 


The defects in Division are nearly allied to those in Defi- 
nition (§ 62). 

In too great width the spheres of the members of division, 
taken together, exceed the sphere of the notion to be divided 
(membra dividentia excedunt divisum; divisio latior est suo 
diviso). The Stoical division of passions (πάθη) into four 
chief forms—laetitia, libido, aegritudo, and metus—is too 
wide, if, according to the definition recognised in that school, 
πάθος is taken to mean ὁρμὴ πλεονάζουσα. The member of 
division goes beyond the sphere of (positive and negative) 
desire, and embraces the feelings also. 

Divisions of men into good and evil, of systems into true 
and false, of actions into voluntary or not voluntary, or of 
temperaments into the four well-known fundamental forms, are 
too narrow, because they disregard the endless number of 
transition forms. The division of natural objects into simple 
and compound overlook the third possibility of organic unity, 
in which we can as little speak of a combination, which pre- 
supposes an original separation and an external conjunction, as 
we can of simple punctual unity. The same fault occurs often 
in disjunctions which are divisions of possibilities. 

A modern division of affections into self-love, affection for 
others, and mutual affection, may serve as an example of faulty 
division whose spheres do not thoroughly exclude each other. 
Mutual affections are those affections for others which are 
returned. They are a subdivision of the second, not a new 
third kind. 

A confusion of different principles of division exists in the 
division of the tenses of the verb into principal and historical 
tenses, used more especially in Greek grammar. The motive 


1 Appetitus vehementior, Cie. Tuse. iv. 6. 


§ 66. Connection between Notions, ete. 185 





for this.illogical division lay, undoubtedly, in the well-founded 
dislike to call the historical tenses merely secondary tenses, 
which would have been actually false, and in the dislike, 
also well-grounded, to denote the one class, by a merely ne- 
gative designation, the non-historical tenses. The tendency, 
arising from a false love of system, to place on either side an 
equal number of classes of tenses, was unjustifiable. It should 
rather have been recognised that the one group of rules hold 
good for one class of tenses, for the historical, namely ; and the 
other group in an essentially similar way for two classes of 
tenses, viz. for the present and future tenses. These two 
classes, however, were not to be opposed to the historical under 
one positive notion, but were to be named in connection with 


each other. 


§ 66. The formation of valid notions and of adequate 
definitions and divisions can only attain to scientific 
perfection in connection with all the other processes of 
knowledge. 


For the formation of general conceptions there is needed the 
combination of particular conceptions only, not of judgments, 
inferences, &c. The combination of the elements of the 
content of the conception does not need to be produced by 
judgments which include them; it is already originally con- 
tained in the perceptions and intuitions. Nor does the separa- 
tion of the content need negative judgments. It results by 
means of the processes of attention and abstraction, which in 
no way presuppose the forms of the judgment. Those who 
mean by notion only a general conception, or a conception with 
an objective reference, are not correct if they make the struc- 
ture of the notion depend on a previous structure of judg- 
ments. The formation of the notion, however, in its fuller 
sense (as a knowledge of the essence) depends upon the for- 
mation of judgments. In order to decide what makes an 
essential, or what makes up the universal and lasting basis for 
the most, and the most important, attributes, one must as- 
certain on what conception the most universal, most exception- 











186  § 66. Connection between Notions, etc. 





less, and most scientific judgments are based. For example, 
the completion of grammatical notions depends upon an in- 
vestigation, requiring ever to be renewed, whether a consistent 
system of universal rules can rest upon the notions we already 
have. The dependence is reciprocal, however. The scien- 
tific judgment also presupposes the scientific notion. For 
example, it is impossible to reach a system of grammatical 
rules in any way satisfactory if a happy tact in forming gram- 
matical notions had not already prepared the way. The 
history of Grammar shows a gradual mutual development of 
notion and rule. In this sense Schletermacher' says rightly— 
the judgment presupposes the notion according to its essential 
existence, and the notion the judgment. The notion which, 
according to the measure of its form, agrees with the object, 
must have before it a whole system of judgments. The 
formation of the notion stands in like reciprocal relation 
to the syllogistie and inductive formation of inferences, to 
knowledge of principles, and to the formation of complete 
systems. Notions like Entelechies, Monads, Stages-of-develop- 
ment, Stages-of-culture, Differential and Integral, Gravitation, 
Chemical Affinity, and the like, presuppose whole scientific 
systems. They again, on their side, condition the develop- 
ment of the systems. We may say ”—the notion must be the 
starting-point, and also the end and aim of all thinking, 
provided that it is not explained with a one-sided RN 
tion, and with unjust disregard of the other function, u of 
their logical analysis, to be “the single product of the mind.’ 
Any one function, in the degree of its own development, 
furthers the development of other functions, and is furthered 
by them. In science at least the mutual advancement of 
every member is no empty delusion. 

But the doctrine of the Notion as the simpler form must 
precede the doctrines of Judgments, Inferences, and Systems, 
without detriment to a real reciprocal relation, and must now 
be brought relatively to a close. 


1 Dial. pp. 82, 83, 402. 
2 With J. Hoppe, Die gesammte Logik, p. 20, Paderborn, 1868. 


§ 67. The Definition of the Fudgment. 





PART FOURTH. 


THE JUDGMENT IN ITS REFERENCE TO THE OBJECTIVE 
FUNDAMENTAL COMBINATI ONS OR RELATIONS. 


$ 67. THE JupGMENT (iudicium, ἀπόξζανσις, as a part 
of the inference it is called propositio or πρότασις) is the 
consciousness of the objective validity of a subjective 
union of conceptions, whose forms are different from, 
but belong to each other. It is the consciousness, 
whether or not the analogous combination exists between 
the corresponding objective elements. As the individual 
conception corresponds to the individual existence, so 
the judgment in its various forms corresponds to and is 
the subjective copy of the various objective relations. 
A judgment expressed in words is an Assertion or Pro- 
position (enunciatio, ἀπόφανσις). 


In the formation of judgments we advance from single con- 
ceptions and their elements to the combination of several. 
The progress here (as “it is also in the combination of judg- 
ments and inferences) is synthetic, while the progress made 
from perception to the formation of individual conceptions and 
notions was analytic. The judgment is the first whole which 
has been again reached by synthesis. Logical theory, how- 
ever, must not begin (as some logicians say) by attention 
to this (derivative) whole, but must first attend to the imme- 
diately given (primitive) whole, i.e. to the perception. 











188 867. The Definition of the Fudgment. 





Neither single notions (absolute or relative), nor mere com- 
binations of notions, are judgments. Conviction conceiving 
the happening or not happening of what is thought, is Judg- 
ment. The Judgment is distinguished from the merely sub- 
jective combination of conceptions by a conscious reference to 
what actually exists, or, at least, to the objective phenomena. 
The reference of thought to actual existence gives the judg- 
ment its character of a logical function. Where the conscious- 
ness of the objective validity is wanting there is no judgment; 
where it is erroneous the judgment is false. 

The formation of a combination of conceptions, and of the 
consciousness of its validity, can be contemporaneous ; but 
the combination of conceptions (e.g. of the conception of this 
criminal with the conception of the deed laid to his charge, and 
of his unlawful intention, which makes him guilty) may be ac- 
companied for a time by the consciousness of the uncertainty 
of its objective validity, until sufficient grounds of decision 
present themselves, which lead to the consciousness of its 
correspondence or non-correspondence with objective reality, 
i.e. to the (affirmative or negative) judgment. 

In mathematical judgments the reference to objectivity is 
never wanting. Our conception of space corresponds to 
objective existence in space, and the geometric judgment is the 
consciousness of the accordance of a (subjective) assertion 
with an (objective) relation of a construction in space. The 
true axiom in actual construction, whether this is realised in 
us or in nature, must prove itself to be objectively valid, in 
each case, in proportion as it is the more exactly constructed. 
The notion of a number, also, although number does not exist 
without our consciousness, has its basis on objective reality, 
viz. on the quantity of the objects, and on the existence of 
genus and species, which compel the subsumption of many 
objects under one notion. The true arithmetical axiom must 
accord with the objective relation of quantity, that when the 
presupposition (hypothesis) is realised the assertion (thesis) is 
realised also. If I take 302. from 100/., and then add 207., 
907. must remain in the cash-box; for in the abstract the 


$67. The Definition of the Fudgment. 189 





------------ 


equation is 100—30+20=90; and the validity of the equa- 
tion is its applicability to all numerical objects possible. 
Numbers can be detached by abstraction from this reference, 
and can be raised to be themselves objects of thought, but in 
this way they attain only a relative independence. 

The assertion made [by Hamilton, Mansel, and others] that 
thought is to be called formal only in so far as it can be con- 
sidered from the side of its form, without reference to the matter, 
is not correct. It is not the thinking, which is considered from 
the side of its form, that is formal, but the logical treatment 
which has to do with the form of the thinking, just as itis not 
language grammatically considered, but its grammatical con- 
sideration that is formal. Thinking in Logic itself is some- 
thing formal, i.e. it is thinking which has to do with the form 
of thinking. Thinking considered and legislated for by Logic, 
is logical thinking when it is logically correct or in accordance 
with the logical laws. It is not a special kind of thinking co- 
ordinate with other kinds. Every operation of thought is 
logically or formally correct when it corresponds with the 
logical laws. Now, in so far as the logical postulate, which 
has to do with the judgment, is concerned—that it may be 
true—formal correctness and material truth coincide in the 
individual judgment. The former can also be limited to the 
mere correctness of the structure (of the conjunction of sub- 
ject and predicate); but it is a proceeding of very little value 
to do so, and to say, for example, that the materially false 
proposition, “all trees have leaves,’ is formally correct. So 
far as the derivation of a judgment from data (which are pos- 
sibly false) corresponds to the logical laws which are valid for 
it, this derivation is formally correct; and the derived judg- 
ment has then been derived with formal correctness, though 
it may not be materially true. The logical correctness of the 
sum total of all the operations of external and internal percep- 
tion aiming at knowledge, though not ¢dentical with the material 
truth (which is the result aimed at by it), is necessarily con- 
nected with the material truth (whether in the fullest or in a 
limited sense of the word). Logic, as such, cannot decide upon 














190 $67. The Definition of the Fudgment. 





the truth of a judgment, because it only enunciates rules, and 
does not itself carry out their application. Its problem is 
legislative only. Logic, as such, has ‘ no exception to take 
against the judgment, ‘all trees have leaves.’ But it is a 
mistake when this is understood to mean,' that the proposition 
is recognised to be “a judgment logically correct according to 
form.’ Logic takes no exception to it, because it has not to 
do with this judgment any more than with any other. The 
application of the logical postulate, that it must have a subject 
and predicate, is to be put into execution by means of a merely 
logical knowledge, but the logical postulate, that it must be 
true, by means of knowledge of natural science, which forces the 
falsehood to appear. ‘ Formal correctness’ is limited to ‘ free- 
dom from contradiction ’ only when the logical rules aim solely 
at this absence of contradiction.? But even in this case Logic, 
as the legislative science, would not decide upon the correct- 
ness (in this sense not at ‘all involving the material truth) of 
any one given judgment, nor expose the single contradictions, 
but would only enunciate the rules for this judicial function. 
As the forms of conception were originally recognised in 
and by kinds of words, so judgments are in and by proposi- 
tions. Plato explains the λόγος to be the revelation of thought 
(διάνοια) by the voice (φωνὴ) by means of ῥήματα and ὀνόματα: 
for thought is, as it were, coined into the sounds which stream 
from the mouth. In the Dialogue Sophistes (more probably 


I By Dr. Cal, in his Lehrb. der propäd. Log., $ 8, Vienna, 1865 
[and Mansel, in his Proleg. Log. p. 258; Rudimenta, 4th ed. pref. 69]. 
Against these statements, cf. J. Hoppe, Die gesammte Logik, § 29, 
Paderborn, 1868. Hoppe believes thinking to be the function of 
translating the objective reality into subjective conceptions. His own 
opposition between ‘notional’ and ‘formal’ thinking is defective. 
Thinking, in Logic, is both ‘ formal ’ because it considers the forms of 
thought, and ‘ notional’ because it attains to notions about them. 

2 Cf. § 3. 

3 Theaet. p. 206 D: τὸ τὴν αὑτοῦ διάνοιαν ἐμφανῆ ποιεῖν διὰ φωνῆς 
μετὰ ῥημάτων τε καὶ ὀνομάτων, ὥσπερ εἰς κάτοπτρον ἢ ὕδωρ τὴν δόξαν 
ἐκτυπούμενον εἰς τὴν διὰ τοῦ στόματος ῥοήν. Shorter and less strictly, 
p. 202 B: ὀνομάτων yap ξυμπλοκὴν εἶναι Ad you οὐσίαν. 


§ 67. The Definition of the Fudgment. τοι 





the work of an early Platonist than of Plato') the proposition 
(λόγος), which is the verbal expression of the thought (διάνοια) ? 
in its simplest fundamental form (e.g. ἄνθρωπος μανδάνει), 
explains the combination of substantive and verb as that 
which corresponds to the combination of thing and action 
(ξυμπλοκὴ or ξύνθεσις ἔκ τε ῥημάτων γιγνομένη Kal ὀνομάτων, 
---ξυντιθέναι πρᾶγμα πράξει δι᾽ ὀνόματος καὶ ῥήματοΞ). 

Aristotle? defines the Judgment (ἀπόφανσις or λόγος ἀπο- 
φαντικός) to be a combination of conceptions in which there is 
truth or falsehood (σύνθεσις νοημάτων, ἐν 7) TO ἀληθεύειν ἢ 
ψεύδεσθαι ὑπάρχει), or, with reference to the verbal expression, 
as an assertion about existence or non-existence:* ἔστιν ἡ 
ἁπλῆ ἀπόφανσις φωνὴ σημαντικὴ περὶ τοῦ ὑπάρχειν ἢ μὴ 
ὑπάρχειν. Aristotle,’ agreeing with Plato, makes the ὄνομα 
καὶ ῥῆμα the elements of the simple judgment. 

In accordance with the Platonic and Aristotelian defini- 
tions, Wolff defines a judgment as® ‘actus iste mentis, quo 
aliquid a re quadam diversum eidem tribuimus vel ab ea 
removemus, iudicium appellatur.” The judgment is formed 
by means of the union or separation of conceptions.’ The 
proposition or assertion (enunciatio sive propositio) is the 
combination of words, corresponding to the conceptions, 
which are the elements of the judgment denoting the union 
and separation of the conceptions and what belongs or does 
not belong to the thing. Wolff, accordingly, demands, as 
Plato and Aristotle had done, three series parallel to each 
other—the combination in things is to correspond with the 
union of conceptions, and this last with the expression. 
Several logicians after Wolff, in order to get rid of the dis- 
junction, ‘ combination or separation,’ in the definition of the 


I Theaet. p. 262 E; 263 D, E. 

2 Soph. 263, Ε. A not very happy abbreviation of Plato’s defini- 
tions in the T’heaet.: τὸ ἀπὸ τῆς διανοίας ῥεῦμα διὰ τοῦ στόματος ἰὸν μετὰ 
9Boyyov. The διάνοια is the ἐντὸς τῆς Ψυχῆς πρὸς αὑτὴν διάλογος 
ἄνευ φωνῆς γιγνόμενος. 

3 De Interp. c. iv. 

6 Log. ὃ 39. 


4 Ibid. c. v. 
7 Thid. § 40. 


ἃ Thick: € BS 
8 Ibid. § 41. 





ent 
SS 


A ma nn 


nn «τος See 





a nn an tn. m -.-.. .-.᾽Ἄ-ὠἬ τ». - 


pa en nae 


m ne i eee an 








192 §67. The Definition of the Fudgment. 





judgment, use the expression, The judgment is the conception 
of a relation between two notions. 

Kant defines the judgment! to be the conception of the 
unity of the consciousness of different conceptions, or the 
conception of their relation so far as they make up one notion, 
or, more definitely,? the way to bring given cognitions to the 
objective unity of the apperception. By objective unity Kant 
understands the mutual connection of cognitions according to 
those categories which the Ego evolves from itself by the 
original activity of its own spontaneity, and by which, as a 
priori forms of thought, the Ego fashions the whole content of 
perception, Objectivity in this sense evidently does not denote 
a reference to a real external world, but only to a kind of 
activity of the ego. Hence this doctrine of judgments, in 
spite of the expression of objectivity which it contains, re- 
veals throughout the subjective character of the Kantian 
philosophy. The view which regards the judgment as merely 
a process of subsuming the special under the universal is very 
prevalent among logicians influenced by Kant. In this sense 
Fries teaches,? the judgment is the knowledge of an object 
by notions, since the notion is added to the object as a cha- 
racteristic, and the object is thereby rendered able to be un- 
derstood. | 

Herbart* believes the judgment to be the deciding upon the 
eapability of uniting given notions. 

Hegel understands by the judgment, the determination 
given to the notion by itself, or the notion making itself par- 
ticular, or the original self-division of the notion into its 
moments, with distinguishing reference of the individual to the 
universal and the subsumption of the former under the latter, 
not as a mere operation of subjective thought, but as a univer- 
sal form of all things. Here again, as in the notion, refer- 
ence to reality is taken to be identity with reality. Hegel dis- 
tinguishes judgments from propositions which do not refer 


ı Log. § 17. 2 Kritik der r. Vern. $ 19. 
3 Syst. der Logik, § 28. 4 Lehrbuch zur Einl. in die Phil. $ 52. 
5 Logik, ii. 65 δ, Eneyel. § 166 ff. 


ὃ 67. The Definition of the Fudement. 193 





the subject to a universal predicate, but only express a 
circumstance, a single action, &c. But in fact every (asser- 
tory) proposition must express a logical judgment. 

Beneke' distinguishes the logical judgment, as the analytic 
act of the subsumption of the particular under the universal, 
from the synthetic bases of the judgment or the combinations 
of conceptions by which knowledge is advanced, which are 
accompanied by those analyses. 
have to do with the syntheses only, which precede the judg- 
ment proper; the logical element is the analytic subsump- 
tion of the less general subject-notion (or subject-conception) 
under the more general predicate notion. For example, in 
the judgment, A is a coward, the combination of the notion of 
A with the notion of his deeds is the basis of the judgment; 
its subsumption under the notion of cowardice is the judgment 
proper. Ulrici in a similar way teaches that the judgment in 
the logical sense is the subsumption of the particular under the 
general,? and distinguishes from it the grammatical proposition 
as the mere expression of a perception or a remark.® But the 
reference to objectivity is, however, essential to every judg- 
ment. It is true or false, according to this reference, but not 
according to a merely subjective subsumption. How the view 
of the subsumption can be united with this, cf. 68. 

Schleiermacher explains the judgment to be that product 
of the intellectual function or of the thinking reason, which 
corresponds to the community of existence or the system 
of the reciprocal influences of things, i.e. of their co-existence, 
their actions and passions. Subject and predicate are related 
as noun and verb. The one corresponds to the permanent 
existence or to an existence contained in itself; the other 
expresses a circumstance, deed, or suffering 


In common life we generally 


an existence 
contained in another. The notion of the predicate is con- 
tained in the subject only in judgments improperly so called. 
The judgment proper proceeds upon a fact, and asserts some- 
thing which is contained only potentially in the notion of the 


1 System der Log. i. 156 ff., 260 ff. 
2 Log. p. 482 ff. 3 Ibid. p. 497. 
O 


a ___ SaaS 


“ 


\ 
nn ne en 





u nn eS “ “ 





— wen 


= -«Φ4-.ο-..-«--ὦ 


u. : ἘΞ 
en τορι ὑπ απ here, 


ee ee Se un a ee 


194 867. The Definition of the Fudgment. 





subject. The primitive judgment asserts mere action; the 
incomplete mere reference to the acting subject; the complete 
a reference also to the object of the action under considera- 
tion.! Schleiermacher’s definition makes justly prominent 
the relation of the subjective element to the objectively real. 
It is defective in this only that it keeps in view too exclusively 
the predicative and the objective relation. The definition of 
judgment, without being vague, i.e. without effacing the limits 
between the judgment and other forms, must be wide enough 
to embrace all the forms of judgment. 

The same may be said of the opinions of Trendelenburg and 


Lotze. 


form, to which action corresponds as the analogous form of 
existence. In the incomplete judgment the action alone is 
originally considered. In the complete judgment, however, 
the subject represents the substance, and the predicate the 
action or the property which carries the fundamental notion 
of the action. 

Lotze® also gives in the same way a too narrow explanation 
of the judgment, when he calls it a conjunction of conceptions, 
whose material is worked up in the logical forms, which cor- 
respond to the metaphysical presuppositions concerning Sub- 
stance, Accident, and Inherence. 

[ J. S. Mill asserts that a proposition is not the mere ex- 
pression of a relation between two ideas, nor of a relation 
between the meanings of two names, nor the referring or 
excluding something from a class. ‚It is the assertion of a 
matter of fact that the set of attributes connoted by the predi- 
cate constantly accompany the set of attributes connoted by the 
subject. But as sets of attributes may be classed under 


Trendelenburg? recognises the judgment to be the logical - | 


§ 68. Simple and Complex $udgments, etc. 195 





and the real ground of the proposition is that when the real 
states connoted by the subject. are found, they are always 
accompanied by the real states connoted by the predicate. 
Co-existence and immediate succession, not subsistence and 
inherence, are, according to Mr. Mill, the real analogues of 
the relation of the subject and predicate in the judgment.! 

Boole? divides propositions into primary and secondary. 
The primary express relations among things, the secondary 
among propositions. The former are also called ‘ concrete, — 
The sun shines; and the latter ‘ abstract, —It is true that the 
sun shines. The difference between the two kinds is one of 
interpretation, not form, and therefore they require different 
methods of expression. | 


§ 68. Judgments are both simple and complex. In 
simple judgmenis the following relations are to be dis- 
tinguished :— 

(1) The predicative, or the relation of subject and 
predicate, i.e. the subjective representation of the real 
relation of Subsistence and Inherence. It comprehends 
under it the following :— 


(a) The relation of the thing to the action or to 
the passion. 

(b) The relation of the thing to the property, 
which is, as it were, an action become per- 
manent (with this must be reckoned the rela- 
tion of the thing to the sum total of those 
attributes which make the content of the super- 


—— nn 


heads, the proposition really asserts or denies a sequence, a 
co-existence, a simple existence, a causation, or a resemblance. 
Propositions whose terms are abstract are no exception. 
The abstract terms stand for attribates which really exist, 
1 Dial. p. 304 ff. 
2 Log. Untersuch. ii. 208, 2nd ed.; 231, drd. ed. 


ordinate notion). 


= ΟΣ 


(c) The relation of the action or property (thought 
as subject) to its nearer determination. 


— 


en ne nn me m mn 


ng 
-- an = 











[' Cf. Logic, i. 96-118, especially pp. 107-110, 115-118. 
2 Laws of Thought, 1854 ed., p. 32 ff. ] 


ον 


3 Log. p. 36. 





























196 § 68. Simple and Complex Fudgments, etc. 





In the so-called judgments without subjects (which 
“are expressed by sentences with ‘ impersonal’ verbs) the 
sum total of the existence surrounding us, thought of 
indefinitely, or an indefinite part of it, takes the place 
of the subject. In the substantial judgments the being 
conceived as inhering, or the existence, takes the place 
of the predicate. | 

(The verbal designation of the predicative relation is 
the grammatical congruence between the subject and 
predicate in the inflection of noun and verb, In the 
case, (a) the grammatical subject is a substantivum 
concretum and the predicate a verb; (b) the subject is 
again a substantivum concretum, and the predicate 
either an adjective or a substantive, with the auxiliary 
verb to be; (c) the subject is a substantivum abstractum, 
and the predicate is either a verb, adjective, or substan- 
tive, with the auxiliary verb. The copula in every 
case lies in the form of inflection. 
to be belongs to the predicate, and is not, as usually but 


erroneously happens, to be considered as itself the 


The auxiliary verb 


grammatical copula. The grammatical agreement of 
its inflection with the inflection of the subject, by means 
of which the forms is, are, &c. come from the infinitive 
to be, is the copula, or the expression of the relation of 
inherence between the predicate and subject. ) 

(2) The object-relation of the predicate to its object, 
i.e. the representation of the real relation of the action 
to the objects towards which it is directed. The change 
of reference to others is contained immediately in the 
essence of the action as the proper change of the sub- 


ject. (Here also the real relation is expressed in the 


Categories of Relation in the Kantian Sense. 197 





logical, and the logical in the grammatical.) The object 
either completes or makes more determinate. The object 
which completes the predicate corresponds to the imme- 
diate object of the action, the object which makes more 
determinate or is adverbial corresponds to an object 
which stands in some mediate relation to the action. 
These relations are those of space, time, modality, 
causality, conditional and concessive, instrumental, con- 
secutive, and final. 

(The oblique cases are the verbal expression of the 
various fundamental forms of the object-relation. The 
accusative, as it appears, originally denoted distance, 
and so the whither or aim of the action; the genitive, 
the whence, and the wherefrom, or the starting-point of 
the action ; and the dative, the where, wherein, and 
whereby, or the place, determination, and means of an 
action. The causal relation was thus originally con- 
fused with the local, just as in the formation of indi- 
vidual conceptions, notions, &c., and in all logical 
operations generally, the elements which arise from 
internal perception are confused with the time- and 
space-form. Some other cases, and prepositions joining 
themselves to the cases, serve to denote the manifold 
modifications of those fundamental forms. ) 

(3) The attributive relation. It is a repetition of the 
predicate, and mediately also often a repetition of the 
object-relation as a mere member of a judgment whose 
predicate is another member. 

(The grammatical agreement in the inflection of nouns 
and verbs is the verbal expression of this relation. When 
the object-relation is added, the use of cases and preposi- 








198 ὃ 68. Simple and Complex Fudgments, etc. 





tions must be combined with this agreement. Some- 
times the cases and prepositions alone (e.g. the Gene- 
tivus possessivus) serve to express the relation; for the 
participial determination added in thought—arising, 
being, &c.—is not to be expressed.) 

The multiple or complex judgment arises from simple 
judgments (as complex propositions from simple pro- 
positions), which are co-ordinate or subordinate to each 
other. Co-ordination belongs both to complete judgments 
(and propositions) and to simple parts of a judgment 
(and proposition). It may be copulative, divisive, and 
disjunctive, comparative, adversative, and restrictive, 
concessive, causal, and conclusive. Subordination rests 
on this, that a judgment (and proposition) is joined to 
another judgment (or proposition) either as a whole or 
with one of its parts. The subordinate judgment is: 
(a) according as it enters into its superordinate, either 
as a whole or with only one of its elements, either an 
infinitive or relative judgment (and accordingly its 
verbal expression, the subordinate proposition, is either 
an infinitive or relative proposition ; the ‘ conjunctional 
proposition’ is logically classed with the former, and 
the ‘pronominal proposition’ with the latter); (b) ac- 
cording to the place which it or the part of it entering 
into the whole judgment (proposition) takes, it is a 
judgment (or proposition) either subjective, predicative, 
attributive, objectively completing or objectively deter- 
mining. The objectively determining or adverbial 
judgments (and propositions) divide again into local, 
temporal, comparative, causal, conditional (or hypo- 
thetical), concessive, consecutive, and final. Several 


Categories of Relation in the Kantian Sense. 199 





judgments (propositions) which are subordinated to 


the same principal judgment (or sentence) may be co- 
ordinate or subordinate to each other, and may be formed 
(e.g.) copulatively-hypothetical, disjunctively-hypothe- 
tical judgments (propositions), &c. 

(Language denotes the relations. co-ordinate and sub- 
ordinate sentences, partly by conjunctions and relative 
pronouns, partly by peculiar syntactical forms. ) 


Logic has hitherto paid attention to a few cases only out of 
the great number of these relations, while Grammar, more 
accustomed to correct itself by the consideration of indi- 
vidual cases, has recognised them for a long time in greater 
completeness, and (by means of the researches of Karl F. 
Becker) has learned to know them more thoroughly.! False 
explanation and a one-sided exaggeration of the logical charac- 
ter of language are always to be rejected. But, to deny the 
assertion of a logical basis of grammatical relation itself, is a 
perverseness which cannot be logically justified, however easily 
it may be psychologically explained. Strepuous battling against 
one extreme easily impels us to the opposite. 

Aristotle discussed the so-called (by later logicians) cate- 
gorical judgments exclusively (he himself understood by the 
categorical judgment the affirmative). The earlier Peripa- 
tetics and Stoics soon brought hypothetical and disjunctive 
judgments within the circle of their logical investigations. 

Kant? based the division of judgments into categorical, 
hypothetical, and disjunctive, on the Category of. Relation— 
Subsistence and Inherence, Causality and Dependence, Com- 
munity or Reciprocity. But this division is by no means 


! Although many points of Becker's doctrine are seen to be false 
from the stand-point of the historical investigation of the development 
of language, the doctrine itself is very serviceable for the logical under- 
standing of language, and is especially useful for that of the structure 
of sentences 


2 Kritik der r. Vern. §§ 9-11; Proleg. 2; Metaph. § 21; Log. § 23. 


m ᾿ 
sins dans ation 


. 2. u am 
ee ; 


ge oN ee, Shee ἐᾶν,» wan 


SS Ss a ae me ~ 











200 ὃ 68. Simple and Complex Fudgments, ete. 





complete, and referring the disjunctive to real reciprocity is a 
mistake. Besides, the Kantian Categories of Relation may 
be naturally compared with the Aristotelian Categories. For 
the latter proceed upon the formal kinds of individual ezist- 
ence, and the former on the formal kinds of relations which 
arise between the different forms of individual existence 
and groups of similar individual existences. The compari- 
son extends similarly to their application to Logic. The 
Aristotelian Categories denote forms of conception, but the 
Kantian Categories of relation establish forms of judgments. 
The defects of the Kantian divis’on have been partly, but not 
sufficiently, recognised and avoided by later logicians. The 
logical meaning of the grammatical relations of the sentence 
has seldom been rightly appreciated.! 

Schleiermacher gives some hints about the mutual dependence 
of relations in simple judgments worthy of consideration. The 
existence which corresponds to the judgment is, according to 
him, the co-existence of things, by means of which every 
one thing is in every other, and acts and is acted on by it.? 
The first moment of judging, or the primitive judgment, asserts 
mere action without reference to a subject which acts, or to an 
object which endures. The place of the subject is occupied by 
the chaotically established sum total of existence. The pri- 
mitive judgment is verbally expressed by the impersonal verb.? 
The advancing construction of the judgment is a passing over 
from the more indefinite to the more definite. If reference to 


| We may say* Logic means by predicate the verb together with its 
objective relations, if such are present. For example, in the proposi- 
tion, A strikes B, it is not the mere striking, but the striking Β, that 
is the logical predicate. But we must, in the predicate so defined, 
distinguish the purely predicative from the objective relation, and give 
to the latter a particular consideration; which consideration belongs 
to Logic and not to Grammar, because it depends upon a special real 
fundamental relation ; mere grammar has to do with the mere form of 
the verbal expression. 


2 Dial. § 139. 3 Ibid. § 304. 





* With Trendelenburg, Log. Unt. 2nd ed., ii. 253. 


Categories of Relation in the Kantian Sense. 201 








the acting subject merely is affirmed the primitive judgment 
passes over to the incomplete: if, further, the fact can be 
traced back to its two co-operating factors, the complete judg- 
ment results, which must, besides the predicative, include also 
the objective-relation.! An absolute judgment is developed 
from the sum of all complete judgments, whose subject is the 
world, or the orderly whole of existence.? The Adjective as 
Epitheton (er Attribute) is the result of an earlier judgment, 
which is already contained as an element in the subject- 
notion.? 

The division of Judgments‘ into Judgments of Content and 
of Extent presupposes that the judgment, as if it were a depen- 
dent form, is to be estimated only according to its relation to the 
forms of the notion (though Trendelenburg himself attributes 
to it a peculiar “antitype in the actual’—the action of the 
substance). This estimation does not wholly include the 
essence of the judgment, and the division falls short of its 
multiplicity of its relations. The judgment, with its flexible 
form, may be of service in the formation of notions; but this 
is not its whole significance. The so-called ‘judgments of con- 
tent’ denote as categorical judgments a relation of inherence, 
and the designation is convenient when the inherence of the 
essential marks is under consideration. Every relation of 
inherence is not to be thought of as a relation of content (e.g. 
the inherence of mere modi and relations is not). As hypo- 
thetical judgments they depend upon a relation of causality, 
whether they denote the connection of a cause with its effect, 
or the connection of several effects with the same cause, or 
the connection founded on the real causal relations of several 


I Dial. ὃ 305. 2 Ibid. δὲ 306-7. 3 Ibid. ὃ 250, p. 197 ff. 

* Cf. Trendelenburg, Log. Unt. 2nd ed., ii. 237 ff. ; 3rd ed.,ii. 261 ff. 
Categorical and Hypothetical Judgments are called ‘ judgments of con- 
tent’ by Trendelenburg ; and Disjunctive Judgments, ‘judgments of 
extent.’ For example, the proposition: Conic sections are regular 
curves, is a judgment of content; but the proposition: Conic sections 
are either circles or ellipses or parabolas or hyperbolas, is a judgment 
of extent. 








202 § 68. Simple and Complex Fudgments, ete. 





objects of knowledge. In any case they correspond to special 
relations of existence, and their meaning does not merely 
express the relation of content. The so-called judgments of 
extent may be reduced to the ‘ judgments of content,’ and are 
recognised to be designations of the relation of what subsists 
to what inheres ; provided only that the true predicate is not 
sought for in the predicate substantive, but (as must happen) 
in the connection of this substantive with existence, and the 
copula not in the auxiliary verb, but in the logical connection 
of subject and predicate and its verbal expression in the gram- 
matical form of inflection. (The so-called ‘judgment of 
extent,’—* Every man is by race either a Caucasian, Mongolian, 
Ethiopian, American, or Malay ’—is equivalent to the judgment, 
< Every man has either the sum total of marks which charac- 
terise the Caucasian, or &c.’ The true predicate is being a 
Caucasian. The expression of the copula lies in the inflection 
only, according to which the form ‘is’ has resulted from the 
form ‘ to be’) This reduction exempts us from the necessity 
either of comprehending under the one notion, or at least 
under the one name of judgment, operations of thought which 
are quite distinct, or with Fries, Hegel, Ulrici, and others, of 
considering subsumption to be the only valid form of judg- 
ment, and so taking this relation out of its natural connection 
with the rest. 

[Sir W. Hamilton, starting from the thought that judgment 
is the subsuming one class under another, and that the pre- 
dicate and subject are respectively greater as the notions are 
taken in their extent and content, divides judgments into two 
classes, according to the relation of Subject and Predicate, as 
reciprocally whole and part. If the subject, or determined 
notion, be viewed as the containing whole, we have an Inten- 
sive or Comprehensive Judgment: if the Predicate notion be 
viewed. as the containing whole, we have an Extensive Judg- 
ment. On this distinction the Comprehensive and Extensive 
forms of Syllogism are afterwards based. ' 

J. S. Mill, who proceeds upon the thought that the most 


[' Lect. on Logie, i. 281. 


Categories of Relation in the Kantian Sense. 203 





important relation of the notion is its connotation of a set of 
attributes, bases on this his attrtbutive theory of propositional 
forms. All propositions express an actual relation between 
two sets of attributes, so that when the one is present the 
other is present or absent. The attributes, e.g. connoted by 
the word ‘man,’ are always accompanied by the attributes 
which are connoted by the word ‘ mortal,’ and so we say ‘all 
men are mortal.’ Mr. Mill’s attributive theory of propositional 
forms agrees to some extent with the comprehensive judg- 
ments of Hamilton; though it has an entirely different point 
of view. It is more nearly related to Trendelenburg’s Judg- 
ments of content as modified by Ueberweg. Mr. Mill has 
noticed the ambiguity which results when the copula is taken 
to be the auxiliary verb ‘is,’ and tries to get rid of it by 
distinguishing between ‘is’ when a mere sign of predication, 
and when it signifies existence. In the proposition, ‘ Socrates 
is just,’ the word ‘is’ may mean either that the quality just 
may be affirmed of Socrates, or that Socrates is, that is to say, 
exists. But the difficulty is better got rid of while the thought 
that the relation of subject and predicate in the judgment 
actually mirrors a corresponding relation in real things, and 
in turn is mirrored by the verbal relation in the proposition, is 
better expressed by saying that the real copula is not ‘is,’ 
but the form of inflection which changes ‘to be’ into ‘is.’ 
For example, in ‘man is mortal’ the real copula is that form 
of inflection which changes the ‘to be’ into ‘is,’ so that, in- 
stead of the unconnected notions, ‘man’ and “to be mortal,’ 
we can say ‘man is mortal.’'] 

The question of debate between Localists and Causalists, in 
reference to the original meaning of the cases, might be 
decided in this way, that the unity of the causal relation with 
that of space (and that of time analogous to it) must be held 
to be the original, and that the stricter separation of the mean- 
ings is later. This principle of the original unity of the causal 
relation with ‘the local is not contradicted but established by 
the historical proof that the nominative in the Indogermanic 


1 Cf Logic, i. 85-87, 107-10.] 


es i um . δ . m GH aS 
a nit ten en en a > Δ - za 
nn un un nr nn nr tee rn he 2 « 3 
En Ze a und ma tlt ce οὐ "3 


ee a 








204 § 68. Simple and Complex Fudgments, etc. 


languages was probably originally formed by an s=sa= this 
(or here) added to the stem; and the accusative by an m= 
amu = yon (or there) (which was dropped in neuters); so that, 
e.g. Rex donum dat is = This here king gives that there gift.! 

The predicate proposition has been named among the sub- 
ordinate complex propositions. They are such sentences as— 
Nonnulli philosophi sunt gui dicant, and the like. That the 
relative proposition here—qui dicant, is, according to its logical 
nature, a predicative sentence, is clear from the transposition— 
multi sunt dicentes, and is especially apparent in cases where 
a proposition of the same kind as a co-ordinate member comes 
in beside a simple predicate, e. g.? Est hic—animus lucis con- 
temptor et istum qui vita bene credat emi—honorem. It is 
here as certain that gui credat is the predicate sentence, as that 
contemptor is the predicate to the corresponding proposition. 
It is only the copula as the expression of the connection between 
subject and predicate, not the predicate, that cannot be changed 
in a subordinate proposition. 

A judgment (and proposition) can never altogether want a 
subject. There may be no distinct subjective conception, and 
in its stead a mere something (it) may enter. Cf. ὕει and Ζεὺς 
ὕει. The indefinite conception of the subject may have been 
the earlier form. | 

The view, that hypothetical and categorical judgments are 
opposed to each other as conditioned and unconditioned is 
combated by some logicians.? Judgments such as—God is 
just, the soul is immortal, do not, they say, involve the asser- 
tion, there is a God or a soul. But-it is a fact that he 
who does not accept the presupposition must add clauses to 
these propositions, which will make them hypothetical ;— 
if there be a (one or several, personal) God, if there be a 
(substantial) soul. A proposition such as—True friends are 


1 Cf the Dissertation of G. Curtius, Ueber die localistische Casus- 
theorie, to the Philological Association of Meissen, 1863. 

2 Virgil’s Aen. ix. 205 sqq. | 

3 Herbart, Einl. in die Phil. § 53; Drobisch, Log. 3rd ed. p. 59 i 
Beneke, Log. 1. 165. 


J 


Categories of Relation in the Kantıan Sense. 205 





to be esteemed, rests on the supposition that there are true 
friends. This presupposition is contained in- the indicative. 
Languages have created other forms for expressing its doubt 
and denial (the Greek, the fullest and strictest). Such a 
clause is superfluous, only when the connection of the whole 
(as in a novel) or the well-known sense of the word (as Zeus, 
Sphinx, chimera) refers to an actual existence merely imaginary. 
Cf. § 85 and § 94. The grammatical question, concerning the 
meaning of a categorical proposition spoken in the indicative, is 
to be strictly distinguished from the logical question about the 
meaning of the categorical judgment. Affirmative judgments 
and such negative ones as only take away a distinct predi- 
cate from the subject (as—this criminal is not guilty) are 
not co-ordinate with (formal or only actually) negative judg- 
ments of such a kind, that the subject-notion is itself thereby 
abolished (as—An absolutely greatest number is impossible). 
The stricter expression for judgments which deny the sub- 
ject itself would be the negation of the objective validity of 
the conceptions and words under consideration (e.g. the word 
magic is an empty sound), or some turn of expression such 
as—there is no absolutely greatest number. The presupposi- 
tion of the reality of the subject is already contained (with the 
above exception) in the categorical expression, and the affırma- 
tion of mere existence in the predicate would amount to a 
tautology. This affirmation can only come in expressly to 
oppose a doubting or denial of the existence of the subject (as 
when it is said—God is, the soul exists). It would then, how- 
ever, be an artificial form quite different from the common use of 
language. The natural mode of expression, when existence is to 
be asserted, prefers other forms—as, e.g. There is a God, equi- 
valent to Es (i.e. etwas, something) ist ein Gott — where the indis- 
tinctly conceived totality of existence, or an indefinite part of it, 
comes in as subject (just as in the sentences it rains, it snows, 
&c.); or where we affirm of the existing subject, its existence 
as something (sunt aliquid Manes), or its existence there, its 
entrance into our neighbourhood, or within the sphere of our 
observation, and more than its mere existence in general. For 
this last is itself implicitly asserted by positing the subject. 


en 


in ee nr er Δ σαν να en m A nn tl 








'% 69. Quality and Modality of Fudgments. 





§ 69. The kind of reference of the combination of 
judgment to actual existence furnishes a basis for the 
division of judgments according to quality and modality. 
We must be conscious in the judgment, as we have 
defined it, whether or not the combination of concep- 
tions corresponds with the reality. The Quality of 
the Judgment rests on the result of the decision, the 
Modality on the degree and kind of its certainty. 
According to quality, judgments are affirmative or nega- 
tive. The notion or idea of affirmation is the conscious- 
ness of the agreement of the combination of conceptions 
with actual existence; the notion of negation the con- 
sciousness of the want of agreement of the combination 
of conceptions with actual existence. According to 
modality, the judgment is problematic, assertory, or 
apodictic. Its problematic character lies in the uncer- 
tainty of coming to a decision upon the agreement of the 
combination of conceptions with actual existence. Its 
assertory character lies in the immediate (based on 
one’s own or another’s perception) certainty; and its 
apodictic character in the mediately acquired (based 
on demonstration, ἀπόδειξις) certainty of coming to such 
decision. 

(Negative particles form the verbal expression of the 
negation ; the moods of verbs and corresponding par- 
ticles, e.g. perhaps, certainly, &c., which all belong to 


oO 
the copula, not to the predicate, express modality. ) 


Aristotle divides! the Simple Judgment (ἀπόφανσις) into 
Affirmation (xatddacis) and Negation (ἀπόφασις). A co- 
existence is predicated in affirmation, a separate existence ın 


' De Int. c. v., vi. 


§ 69. Quality and Modahty of Fudgments. 207 











negation (karabacis ἐστιν ἀπόφανσίς τινος κατά Twos, ἀπό- 
φασις δέ ἐστιν ἀπόφανσίς τινος ἀπό twos). A negative sub- 
ject-notion (d:oua ἀόριστον) or ἃ negative predicate-notion 
(ῥῆμα ἀόριστον) may enter into the affirmation or negation.' 
The negation which negatives the judgment itself, and not a 
single notion in the judgment, belongs to the copula. Hence 
the Schoolmen enunciated the Canon—In propositione negativa 
negatio afficere debet copulam. 

Wolff also only distinguishes the classes—affirmative and 
negative judgments, and teaches that when the subject or 
predicate only, and not the copula, is affected by the negation, the 
judgment appears to be negative, but is not so. He calls such 
judgments propositiones infinitas. In the same way Reimarus 
speaks of “ propositiones infinitae ex parte subiecti vel prae- 
dicati.’? 

Kant divides judgments according to Quality into affirma- 
tive, negative, and limitative or infinite, according to the three 
Categories of Quality, Reality, Negation, and Limitation. He 
understands by the limitative or infinite judgment one in which 
the negation is connected, not with the copula, but with the pre- 
dicate. (He has not noticed judgments with negative subjects. ) 
Judgments of that kind belong rather partly to affirmative and 
partly to negative judgments, as the union of the subject with 
the negative predicate is affirmed or denied. Kant has been 
led to this triple division by his love for the schematic regularity 
of his Table of Categories.? 

The division of judgments from the point of view of modality 
into assertory, apodictic, and problematic, has been founded on 
the Aristotelian division : πᾶσα πρότασίς ἐστιν ἢ τοῦ ὑπάρχειν 
ἢ τοῦ ἐξ ἀνάγκης ὑπάρχειν ἢ τοῦ ἐνδέχεσθαι ὑπάρχειν. But 
this division has to do with the analogous objective relations 
rather than with the subjective degree of certainty. Such a 
determination as ἐξ ἀνάγκης, and also ταχέως, &c., is called 
τρόπος by Ammonius, modus by Boéthius. 


I De Interpr. c. x. 2 Vernunftlehre, $ 151. 
3 Kritik der r. Vern. §§ 9-11; Proleg. ὃ 21; Log. ὃ 22. 


4 Anal. Pr. i. 2. 





208 § 69. Quality and Modalhty of Fudgments. 





Kant' bases the division according to modality upon his 
modal categories—Possibility and Impossibility, Existence and 
Non-Existence, Necessity and Accidentality. In this, how- 
ever, the combination of Impossibility, which is a negative 
necessity, with Possibility and also Accidentality, which de- 
notes existence not recognised to be necessary, with Necessity, 
is inexact. The knowledge of Impossibility is not a pro- 
blematic, but a (negatively) apodictic judgment (which Kant 
in the application has himself recognised, since, in his Knit. der 
r. Vern. p. 191, he considers the formula—it is impossible, to 
be the expression of apodictic certainty). The knowledge of 
the accidental is not an apodictic but an assertory judgment. 
Besides, Kant has not sufficiently distinguished the subj ective and 
objective element in the Categories of Quality and Modality. 

The Relation of the subjective and objective elements in the 
act of Judgment is not the same in Quality and Modality as 
it is in Relation. The Cafegories of Relation are notions 
of forms of existence and of relations between objective ex- 
istences which are mirrored in the corresponding relations of 
the judgment. Quality and Modality, on the other hand, have 
to do with the various relations which exist between the com- 
bination of conceptions and what actually exists. Non-existence 
does not exist as a form of what is. What is thought in 
a true negative judgment does not exist. The notion of non- 
existence may be applied to what is represented as existing 
without actually existing, only in so far as the subjective 
picture does not correspond to the objective fact. In this sense 
Aristotle rightly says—ov yap ἐστι τὸ ψεῦδος καὶ τὸ ἀληθὲς ἐν τοῖς 
πράγμασιν ἀλλ᾽ ἐν τῇ διανοίᾳ---ἡ συμπλοκή ἐστι καὶ ἡ διαίρεσις 
ἐν διανοίᾳ, ἀλλ᾽ οὐκ ἐν τοῖς πράγμασιν" Cf. Trendelenburg.3 
‘ The Logical negation roots itself in thought only because 
it never can find itself pure and without support anywhere in 
nature.’* ‘ Pure negation belongs to thought only.’ | 

But we cannct wholly agree with Aristotle, when’ he seeks a 


| Kritik der r. Vern. $$ 9-11; Proleg. $ 30; Log. ὃ 30. 
2 Metaph. vi. 4, §§ 4-6. 3 Log. Unters. 2nd ed. i. 44. 
4 Ibid. ii. 148. ® Metaph. ix. 10, § 1. 


§ 69. Quality and Modality of Fudgments. 209 








form of existence as a correlate to negation, and thinks that 
separation in things corresponds to it. Separation actually 
takes place (and the state of separation is a real occurrence), 
and is rather to be expressed in a positive judgment. A 
negative judgment does not therefore imply a separation in 
things. (The sum of the angles of a plane-rectilineal triangle 
is neither more nor less than two right angles, the diagonal 
of a square is not commensurable with its side; but the 
former does not therefore separate itself from 2 sum which is 
greater or less than two right angles, nor the latter from com- 
mensurability.) In real things which are the objects of our 
thought there is a positive opposition or strife between con- 
trary opposites; but conceptions and negations exist only 
in so far as mental essences, which themselves conceive and 
think, form the object of our conceptions and judgments ; 
and analogues of conceptions and negations exist only in 
so far as the tendencies motions and desires, which dwell in 
inanimate objects, bear in themselves, as it were, a picture of 
what shall be, and this picture in consequence of hindrances does 
not arrive at realisation (e.g. an arrested motion or a blighted 
flower). In such a case the picture comes into objective com- 
parison with the external actual existence, and is not merely 
placed in comparison with it by us. When our combination 
of conceptions is established by an objective tendency which 
in consequence of hindrances is never realised, it becomes most 
conformable to nature; for example, Your letter has not 
reached me; This flower does not bloom. It is not limited, 
however, to this one case. 

The negative judgment, when its construction does not 
result from caprice, presupposes that the question to which it 
may be considered the answer is not absurd ;—that some 
motive may be thought for the affirmation ;—and in general 
that at least the genus-notion, under which the questioned pre- 
dicate notion falls, belongs to the subject as predicate. 

The case of Modality is analogous.. The modality on which 
the distinction of problematic assertory and apodictic judg- 
ments rests, exists only in the comparison of our combinations 


P 








210 § 69. Quality and Modality of Fudgments. 





of conceptions with reality. Our decision of affirmation and 
negation rests either upon perception, or upon authentic 
witness which does instead of one’s own perception, or upon an 
inference from another judgment. In the first case we judge 
assertorically. In the last we know either the whole of the 
moments on which the decision must be based, when we can 
give an apodictic judgment; or only a part of them, in which 
case we attain to a merely problematic judgment. Possibility, as 
something objective, must always be distinctly separated from 
subjective uncertainty, and is done so in common language.' 
The Greek language (e.g.) denotes by δύνασθαι (to be capable) 
possibility in the objective sense, and by ἴσως (perhaps), or by 
the optative with ἄν, the (subjective) uncertainty, or the proble- 
matic character, of the judgment, while ἐνδέχεσθαι denotes the 
objective possibility on the side of its external conditions from 
their negative side,—i.e. it agrees with the circumstances, it leads 
to nothing impossible, or nothing prevents that it should be.’ 
Possibility in the objective sense rests on this, that among the 
moments upön which realisation depends there is established 
an essential separation, not merely subjective by our knowledge 
of the one and ignorance of the other, but also objective by the 
nature of the case. The sum total of these circumstances, or 
the total cause, is generally divided into the (internal) reason 
and the (external) conditions. For example, the total cause of 
the growth of a plant divides into the organic power which 
lies in the seed—the (internal) reason, and the chemical and 


1 Cf. Trendelenburg, Log. Unt. ii. 157. 

2 Waitz says (Ad Arist. Org. i. 376) τὸ δυνατόν is the physically 
possible, τὸ ἐνδεχόμενον the logically possible, the problematical. This 
definition, so far as it refers to δυνατόν, is correct, but not strict as 
Waitz himself admits that it does not quite har- 


monise with Aristotle’s actual usage when he thinks that Aristotle 
‘saepius alterum cum altero confundit.’ Our definition given above 
may correspond better. Cf. Arist. Anal. Pr. i. 18, p. 32 a, 18: 
λέγω δὲ ἐνδέχεσθαι καὶ τὸ ἐνδεχόμενον, ov μὴ ὄντος ἀναγκαίον TE- 
θέντος δὲ ὑπάρχειν, οὐδὲν ἔσται διὰ τοῦτ᾽ ἀδύνατον. The δύνασθαι 
denotes the presence of the internal reason, the ἐνδέχεσθαι the presence 
of the external conditions and the absence of hindrances. 


’ ͵ 
regards ἐνδεχόμενον. 





$ 69. sid and ERBEN of Fudgments. 211 





physical powers of air, earth, and light—the (external) condi- 
tions. When the reason is present alone, or the conditions 
alone, possibility arises ; where both are present together fliers 
is necessity in the objective sense. In this sense the poctbilit 
(or capability) of the existence of the oak is contained i ei 
acorn. The historical genesis depends on the advance Feen 
an objective possibility (potentia) to actuality. It is pos- 
sibility in the objective sense that Buhle speaks of. e.g es 
he! explains the opinion to be erroneous, that BE Pe 
with the pure Platonic and Aristotelian philosophy was u 
brought about by learned Greeks crossing over into ἫΝ ὮΝ 
by their literary activity, and says, ‘ They only brought spite 
its possibility because they brought with them lie re of 
Plato and Aristotle, and taught people to understand them 
in the original language, so that sooner or later an un- 
prejudiced person who studied them could remark the differ- 
ence between the kind of philosophy taught in each and the 
kind which had been formed from them.’ Again, it is the re 
establishment of the conditions and the objective oe ii 
a * perhaps’ (subjective uncertainty), that is meant aes we 
say to a boy—I know that it is possible to solve this problem; 
you can solve it (you have the ability to solve it). The netvibes 
that possibility is something objectively real does not contain 
the contradiction that the same thing is called both merel 
possible and also actual. For the occurrence is possible ; but ι 
possibility actually exists in the object of our thinking ie a ae 
complex of causal moments, which is objectively separated 
from the others whose presence makes the pie ean as 
sary. This real possibility, however, as such, is not expressed 
in a problematic, but most commonly in an assertory sales 
by means of the verbs—can, is capable, &e.; just as the teal 
necessity in an assertory judgment is expressed by means of 
the verbs—must, is necessary, &c. (which then belong to the 
predicate, and not, like the ‘ perhaps,’ to the copula). 7 

But a problematic judgment may be based upon our know- 


: Gesch. der neuern Philos. seit der Epoche der Wiederherstellung der 
Wiss. ii. 123, Gott. 1800. | 





212 § 69. Quality and Modalıty of Fudgments. 








ledge of an objective possibility, and an apodictic judgment 
upon our knowledge of an objective necessity ; for what ai = 
sible may perhaps occur, and what 1s necessary will certainly 
occur. A negative judgment is most conformable to nature 
when it is based on an objective negation in the sense given 
above, or on a tendency which is never realised ; but it 1s not 
confined to this relation, In the same way the problematic 
judgment is most conformable to nature where the subjective 
uncertainty about any occurrence, property, &c., rests on a 
known objective possibility—i.e. when the subjective separation 
of the part of the total cause known and of that unknown > 
us (or of what is kept in view by us and of what has not, : 
first at least, been brought into consideration ) corresponds 
strictly with the objective separation of the internal cause 
and the conditions. Wherever we know assertorically that 
the occurrence can happen or has objective possibility, we 
naturally use the problematic judgment about the occurrence, 
that it perhaps will happen. The application of the pro- 
blematic judgment, however, is not limited to this one relation, 
but occurs wherever we have any ground of probability and no 
absolute hindrance, i.e. know no cause of impossibility. In the 
same way, the apodictic judgment is most complete, and yields 
the highest satisfaction to the mind in its search after know- 
ledge, when it rests on an insight into the real genesis from 
the internal cause and the external conditions. Wherever we 
know the presence of this objective necessity of an occur- 
rence, we ought to express the subjective necessity, that it will 
happen, in an apodictic judgment. The application of the ae 
dictic judgment goes beyond this one relation, however, an 
embraces all subjective mediate certainty, even when it has been 
reached in another way (e.g. by indirect proof). The assertion 
of an objective possibility, or of an objective necessity, belongs 
to the matter or content of the judgment because it belongs to 
the predicate, but the problematic or apodictic character belongs 
to the form of the judgment. Aristotle, in his De Interpreta- 
tione and in his Analytics, treats of such ‘ modal’ modifications 
of judgments as really belonging to their matter or content, and 


§ 69. Quality and Modality of Fudements. 213 





do not concern the logical theory of judgments. The modal 
difference, however, of problematic, assertoric, and apodictic 


form does concern logical doctrine. 


In a monograph of Gustav Knauer! Affirmation and Nega- 
tion are traced to Modality. Both are, in fact, to be regarded 
from the same point of view. They have not to do, as Relation 
has, with the different objective relations which are mirrored 
in the judgment, but with the various relations of the subject 
to the object. Accordingly, Knauer calls negation in a nega- 
tive judgment ‘ modal negation,’ and distinguishes it from 
‘qualitative negation,’ which rests on the opposition—not of 
reality and negation, but—of the positive and the negative con- 
trarily opposed to it, as black to white, vice to virtue. ( This 
distinction corresponds to that of Trendelenburg, between 
‘logical negation’ and “real opposition.’) In a similar way, 
Knauer understood by the “ limited judgment,’ one in which 
the predicate is saddled with a limiting determination, which 


can be expressed either by a positive adverbial addition (as in. 


bright red, dark red, half right), or by a ‘ qualitative not,’ 
strictly to be distinguished, however, from the ‘modal not.’ 
But Knauer has overlooked this, that the logical division of 
judgments has to do with differences which belong to the form 
of the judgment, as such, and not with differences belonging 
to any form whatever of notions entering into the judgment. 
Whether man or not-man, red or bright-red, &c., is the pre- 
dicate of a judgment, makes a difference in the form of the 
notions under conside:ation, and in the content of the judg- 
ment. It makes no difference in the form of the judgment 
with which the logical division of judgments has alone to 
do. Accordingly, the rectification of the Kantian Table of 
Categories attempted by Knauer—the substitution of Positive 
and Negative for Reality and Negation— contradicts the 
general point of view, according to which the Categories con- 


' Conträr und contradictorisch, nebst convergirenden Lehrstücken, 


festgestellt und Kant’s Kategorientafel berichtet, Halle, 1868. Well 


worthy of attention, although making some mistakes in what is new, 
and often erroneously believing a correct statement to be new. 


τι τ me ee z 
AS = 
ne 

h e ~~ 


























214 § 70. Ouantıty. 





dition the various functions of judgment. Reality and Nega- 
tion are not, of course, like Substantiality and the other Cate- 
gories of Relation, valid as forms of actual existence. They 
only denote a relation between our thoughts and actual exist- 
ence. This, however, only justifies the attack upon the Kantian 
table of Categories, not Knauer’s own doctrine. On the other 
hand, the axiom of Knauer’s is correct (in which he recognises 
the ‘master of Stagira’ as his ally, but which is not a new 
doctrine, even in the sense that it had been lost sight of since 
Aristotle, and was first brought to light again by Knauer), that 
necessary contradiction exists only between affirmation and 
negation of the same thing, and not between judgments 


whose predicates are opposed contradictorily. See δὲ 77-80. 
[Sir W. Hamilton, with Mansel and Thompson, refuse to 
recognise the modality of judgments as any part of their logical 
treatment. The mode, they say, belongs to the matter, and 
must be determined by a consideration of the matter, and 


therefore is extralogical.' | 


§ 70. Quantity is the extent in which the predicate 
is affirmed or denied in the sphere of the subject-notion. 
Some logicians divide judgments according to Quantity 
into Universal, Particular, and Singular. Singular judg- 
ments are to be subsumed under the other two classes : 
under the first when the subject is definite and indivi- 
dually designated (e.g. Caesar, or this man); under the 
second when the subject is indefinite and designated only 
by a general notion (e.g. a man, ora great general). 
For in the first case the predicate is affirmed or denied 
of the whole sphere of the subject (which in this case is 
reduced to an individual), and in the other case of an 


indefinite part of the sphere of the subject-notion. 


_ [EP Cf. Hamilton’s Lect. on Log. i. 257; Mansel’s Aldrich’s Rudi- 
menta, 4th ed. p. 46 n.; Proleg. Log. 2nd ed. Note H.] 


§ 70. Quantity. 215 
Aristotle distinguishes Universal, Particular, and Indefinite 
Judgments: πρότασιε---ἢ καθόλου, ἢ ἐν μέρει, ἢ ἀδιόριστος-." 
The Judgment Indefinite according to quality, which Aris- 
totle makes co-ordinate with the Universal and Particular, is 
not properly a third kind, but an incomplete, or ἐροίμμμδονοῖν 
expressed, Judgment.? Kant recognised three kinds—Singular 
Particular or Plurative, and Universal J udgments—and EEE 
them to the three Categories of Quantity—Unity, Plurslity 
and Universality. He teaches that singular judgments belon 7 
to the same class as the universal.? i ° 
Herbart says, that individual judgments are only to be 
reckoned along with universal ones when they have a distinct 
subject. When the meaning of a general expression is Es 
by the indefinite article to any individual not more definitel 
designated, those judgments are to be reckoned with the we 
cular.* This manner of reduction shows itself to be the correct 
one, partly in itself, because it does not depend upon the absolute 
number of subject-individuals, but on the relation of this num- 
ber to the number of individuals falling under the subject- 


notion generally ; partly in its application to the forms of 
inference.° 


The subject of the particular judgment is any part of the 
sphere of the subject-notion, and at least any single individual 
falling under this notion. Its limits may be enlarged up to 
coincidence with the whole sphere, so that the partion judg- 


ment does not exclude, but comprehends, the possibility of the 
universal, 





The rule that the judgment, indesignate in reference to 
quantity, is universal if affirmative, and particular if negative 
5 3 


is ia grammatical than logical, and not unconditionally 
valid. 


Anal. Pri. i. 1. 

| [Cf. Hamilton’s Lect. on Log. i. 243.] 

ὅ Krit. d. r. Vern. §§ 9-11; Proleg. ὃ 20; Logik, $ 21. 
Lehrbuch zur Einl. in die Phil. § 62. 
Cf. below, § 107. 




















“ey > 5 
om = - 
een ge =) 


we rung 


διὰ, ταν, 7 











216 § 71. Combination of Divisions, ete. 





§ 71. By combination of the divisions of judgments 
according to QUALITY and QUANTITY four kinds arise :-— 


1. Universal Affirmative of the form—aAll 5 are P. 

2. Universal Negative of the form—No ὃ is P. 

3. Particular Negative of the form—Some S are P. 

4. Particular Negative of the form—Some 8S are 

not P. | 

Logicians have been accustomed to denote these forms 
by the letters a, e, i, o (of which a and i are taken from 
affirmo, e and o from nego). . It will be seen from a 
comparison of spheres, that in every universal judgment 
the subject is posited universally, and particularly in 
every particular judgment; but the predicate is posited 
particularly in every affirmative judgment, or, if uni- 
versally, only by accident (for, according to the form of 
the judgment, both in a and i its sphere can lie partly 
outside of the subject), and universally in every nega- 
tive judgment (for in e the sum total of 5, and in o the 
part of S concerned, must always be thought as separated 
from the whole sphere of the predicate). 


The judgments of the form a (SaP—All 5. are P) can be 
represented in a scheme by the combination of the two follow- 
ing figures :— 


a, 2. Ρ Θ, 2. 


The following scheme is for judgments of the form e (Se P 
_N 8 ia P):— 


PO ΟΣ 


P 


The Four Forms of Fudgment, A, E, I, and O. 217 





J udgments of the form i (Si P—At least a part of S is P) 
require the combination of the four following figures (of 


which 1 and 2 are peculiar to the form i, but 3 and 4 repeat 
the schema of the form 4) :— 


1 j 


51. 

i, 3. 
Judgments of the form 0 (So P—At least one or some S are 
not P) are to be represented by the combination of the three 


following figures (of which 1 and 2 are peculiar to the form o, 
while 3 repeats the schema of the form Θ :— 


© 


If the definite be denoted by a continuous, and the indefinite 


0, 1. 
0, 3. 


by a dotted line, the symbol of judgments of the form 4 may 
be reduced to the one figure :--- 














218 71. Combination of Divisions, ete. 


The Symbol for the judgments of the form i under the same 


presupposition :— 





The use of these Schemata is not confined to that ap- 
prehension of the judgment which finds it to be only a sub- 
sumption of the lower subject-notion or conception under the 
higher predicate-notion, and which, therefore, requires that the 
predicate-notion be made substantive in cases where this is 
actually unsuitable. If the predicate-notion is the proper 
genus-notion of the subject, it is quite natural to take it for 
substantive, but not when it denotes a property or action. 
This last case does not require to be reduced to the first for 
the sake of a comparison of spheres. It is not necessary 
(although in many cases very convenient) to attach such a 
meaning to the circle P as to make it embrace the objects 
which fall under the substantive predicate-notion. The 
sphere of an adjective or verbal conception can be also under- 
stood by the sphere P. It may mean the sum total of the 
cases in which the corresponding property or action occurs, 
while S may denote the sphere of a substantive conception— 
the sum total of the objects in which the corresponding pro- 
perty or action occurs. On this presupposition the coincidence 
of the circles or parts of the circles is not to be taken to 


be the symbol of the identity of objects, but as the symbol of 


the co-existence of what subsists and what inheres.. Cf. § 105. 

In a, 1 all S are only a part of P, but in a, 2 all Sare all P; 
in i, 1 some S are some P, &c. The Quantification of the 
Predicate consists in paying attention to these relations. It 


§ 72. Contradictory and Contrary Opposition, etc. 219 





has been carried out by Hamilton on the basis of assertions of 
Aristotle,’ and according to partial precedents in the Logique 
ou l’Art de penser,? and in Beneke? Cf. § 120. ü 

For the use of these Schemata as aids in the demonstration 


of the theorems which have to do with inference, cf. $ 85 and 
§ 105 ff.; cf. also $ 53. 


$ 72. Two judgments, of which the one precisely 
affirms the very thing which the other denies, are CoN- 
TRADICTORY to each other, or are contradictorily opposed 
(1udicia repugnantia sive contradictorie opposita). Con- 
tradiction is the affirmation and denial of the same 
thing. Judgments are opposed to each other diame- 
trically, or as CONTRARIES (contrarie opposita), which, 
in reference to affirmation and negation, are as different 
as possible from each other, and, as it were, stand furthest 
apart. Judgments should be called SUBCONTRARIES, the 
one of which particularly affirms what the other, agree- 
ing with it in other respects, particularly denies. Judg- 
ments are SUBALTERN (iudicia subalterna), the one of 
which, affirmatively or negatively, refers a predicate to 
the whole sphere of the subject-notion, while the other 
refers the same predicate in the same way to an inde- 
finite part of the same sphere. The former is called 
the subalternant (iudicium subalternans), the latter the 
subalternate judgment (iudicium subalternatum). 

Aristotle defines‘—éotw ἀντίφασις τοῦτο" κατάφασις καὶ 


» [4 ψ' . / u . © 

ἀπόφασις αἱ ἀντικείμεναι. He distinguishes contradictory oppo- 
an > A > ~ 

sition (ἀντιφατικῶς ἀντικεῖσθαι" ἡ ἀντικειμένη ἀπόφανσι5) from 


2 Par. 1664. 
3 Cf. upon this Trendelenburg, Zog. Unters. 2nd ed. ii. 304-307 
and Appendix B. 
4 De Interp. c. vi. 


! De Interp. e. vii. 











220 § 72. Contradictory and Contrary Opposition, etc. 





contrary (ἐναντίως ἀντικεῖσθαι" ἡ ἐναντία ἀπόφανσις). Judg- 
ments with the same content of the forms a and Ο (S a P and 
So P) stand to each other in the relation of contradictory 
opposition, and so do judgments of the forms e andi (SeP 
and SiP). Judgments of the form and e (Sa P and Se P) 
stand in the relation of diametrical or contrary opposition. The 
relation between the forms of judgment i and o (Si P and 
SoP) Aristotle calls only apparently analogous,' κατὰ τὴν 
λέξιν ἀντικεῖσθαι μόνον. Later logicians call such judgments 
προτάσεις ὑπεναντίας, iudicia subcontraria. Aristotle arranged 
the four forms of judgment,? πᾶς ἐστιν ἄνθρωπος δίκαιος (8), 
οὐ πᾶς ἐστιν ἄνθρωπος δίκαιος (0), πᾶς ἐστιν ἄνθρωπο“ οὐ δίκαιος 
(0), οὐ πᾶς ἐστιν ἄνθρωπος οὐ δίκαιος (1), according to the an- 


nexed scheme :— 
a -—O 














i e 

The judgments a and e, which stand furthest apart from 
each other, according to their mutual relations, and in the 
same way the judgments i and 0, are thus set at the opposite 
ends of the diagonal or διάμετρος. In this scheme all the 
above-mentioned relations of judgments are thus arranged :— 


a opposit. contradict. o 


i opposit. contradict. Θ 


Modern Logicians represent these relations in. the following 
scheme (which is found in Boéthius, and, with some difference 


I Anal. Pr. ii. 15. 2 De Interp. x. 19 B, 32-36. 


§ 73. The Matter and Form of Fudgments. 221 





of terminology, but with the same position of the forms of 
judgment, in Apuleius) :— 


a opposit. contraria 


Dr, 


Os ve 


"ὡ 
[Ὁ] 


i opposit. subcontrar. O 


This is less convenient because contraries do not lie at the 
opposite ends of the diameter, but in another view is better. 


$ 73. The matter or content of our judgments is 
obtained immediately through external and internal 
perception, mediately by inference. In the act of judg- 
ment the forms, which are designated by the Categories 
of relation, are imposed upon this matter. We recog- 
nise these forms :— 

(a) First and immediately in ourselves by means 
of internal perception. For example, the relation of 
what inheres to what subsists is recognised in the rela- 
tion of the individual perception or individual feeling or 
volition to the totality of our existence or to our ego, 
the relation of causality to dependence in the relation 
of our will to its expression, &c. 

(b) In the personal and impersonal essences without 
us, on the ground of its analogy to our own internal 
existence. 

The notional apprehension of these forms, in their 
separation from the content, with which they are com- 
bined, comes afterwards, by means of abstraction. 




















222 ὃ 73. The Matter and Form of Fudements. 


The objective validity of these forms is warranted by 
the same moments, and lies under the same limitations 
and gradations, as the truth of internal perception and 
its analogues (§ 41 ff.), as the truth of the conception of 


individuals (§ 46), and as the notional knowledge of the 
essential ($ 57). 

Kant believed these forms to be ἃ priori, or originally inher- 
ent in the human understanding (Stammbegriffe des Ver- 
standes). Before his time knowledge a priori meant, agree- 
ably to the Aristotelian idea, knowledge from causes which 
are the prius natura (πρότερον φύσει), and knowledge a pos- 
teriori, knowledge from effects which are the posterius natura 
(ὕστερον φύσει), and therefore knowledge from immediate expe- 
rience and by testimony (for this knowledge is a kind of know- 
ledge from effects). 

Leibniz identifies! connaitre ἃ priori and par les causes. 
He calls? ratio 4 priori that reason which is the cause 
not merely of our knowledge, but of the truth of things 
themselves. He distinguishes ‘prouver a priori par des 
démonstrations’ (which, of course, is sufficient only when 
‘démonstrations’ mean syllogistic deductions from known 
real reasons), and ‘A posteriori par les expériences.’ He 
recognises the Axiom of Identity and Contradiction (the 
element A priori) to be the only ‘principe primitif’ for all 
knowledge co-ordinate with experience (the a posteriori 
element);* but later adds the Principle of Sufficient Reason.‘ 
The same use of the terms is also found in Leibniz, ap- 
plied to mathematics, in a very instructive passage of his 
Epistola ad Jacobum Thomasium,? in Leibniz’s edition of the 
work of Nizolius, De veris principiis et vera ratione philoso- 
pbandi:° ‘Si rem cogitemus curatius, apparebit demonstrare 
eam (sc. geometriam) ex causis. Demonstrat enim figuram 

| Theod. i. ὃ 44, e.g. 2 Nouv. Ess. ii. 17. 

Réflexions sur Essai de Locke, 1696. 
Theod.i. ὃ 44,1710; Monad. ὃ 32, 1714. 5 Published in 1669. 

> Opera Phil. Leib., ed. Erdman, p. 51. 


§ 73. The Matter and Form of Fudgments. 223 





ex motu, e.g. ex motu puncti oritur linea, ex motu lineae 
superficies, ex motu superficiei corpus. Ex motu rectae super 
recta oritur rectilineum. Ex motu rectae circa punctum im- 
motum oritur circulus, &c. Constructiones figurarum sunt 
motus; iam ex constructionibus affectiones de figuris demon- 
strantur. Ergo ex motu, et per consequens ἃ priori et ex causa.’ 

Wolff says, very insufficiently :' utimur in veritate proprio 
Marte eruenda vel solo sensu; vel ex aliis cognitis ratioci- 
nando elicimus nondum cognita: in priori casu dicimur veri- 
tatem eruere ὦ posteriori, in posteriori autem ἃ priori. He 
adds that experience has to do with the individual only, but 
yet supplies us with the principles from which those indi- 
vidual cognitions, which are not to be reached by immedi- 
ate experience, must be derived ἃ priori. Only by such a 
‘connubium rationis et experientiae’ can the trifling Scholas- 
tic formulae be avoided, and be taught ‘non ex proprio ingenio 
conficta, sed naturae rerum consentanea.’ 

Kant? holds that knowledge which has been reached by a 
general rule, if this rule be itself derived from empirical 
sources, is only relatively to be considered knowledge 4 priori. 
He, for his part, will “not understand such knowledge to be a 
priori which is independent of this or of that experience, but 
only knowledge which is absolutely independent of all experi- 
ence. Opposed to it is every kind of empirical knowledge, or 
knowledge possible only a posteriori, i.e. by experience.’ Kant 
has narrowed the notion ἃ posteriori in its relation to the 
Aristotelian knowledge from effects, or from the ὕστερον φύσει 
(but has done so in accordance with the use prevailing in 
Leibniz and Wolff). He understands by it, knowledge from 
one kind of effects (viz. from those which affect our senses). 
He has given an entirely new meaning (which has since come 
to be the prevailing one) to the expression ἃ priori (partly 
determined by Wolff and Baumgarten, and partly on the other 
side by Hume). He denotes by it, not the opposite of know- 
ledge from effects, but the opposite of knowledge from experi- 
ence. By combining the distinction of knowledge a priori and 


| Log. ὃ 663. 2 Kritik der reinen Vern., Einl. i. 


en ..».» 


rn EEE u OE se nn 


nn 


Se en er 








224 873. The Matter and Form of Fudgments. 





ἃ posteriori with the division of judgments into synthetic and 
analytic (cf. § 83), Kant finds three kinds of judgments— 
1. Analytic judgments, or explanatory judgments, which, as 
such, are all judgments ἃ priori; 2. Synthetic judgments a 
posteriori, or enlarging judgments, which are founded - 
experience; 3. Synthetic judgments a prior, which foun 
themselves on the pure forms of intuition or the pure notions 
of the understanding, and ideas of reason. But those judg- 
ments which Kant calls synthetic judgments a priori are not, 
in fact, formed independently of experience, but are made in 
this way. that we complete the sense-perception by the pre- 
supposition of a causal interdependence (cf. § 140). = 
teaches rightly —That an element arising from within, an > 
this sense & priori, is added to the sensible or ἃ posteriori, - 
wrongly—1. That the ἃ priori element is independent 0 
internal experience; and 2. That it does not belong to things 
in themselves. ἊΝ : ΝΑ 
The Kantian use of the expressions & priori and a posterior, 
which at present prevails, has done more damage than good. 
Kant’s mysterious fiction of a ‘ knowledge ἃ priori, which he 
took to be absolutely independent of experience, and his use of 
the term “ ἃ priori,’ often confounded with the old meaning of 
the term, has produced numberless obscurities and paralogisms, 
from which the Kantian and almost the whole post-Kantian 
Philosophy suffers. A return to Aristotle's meaning were better. 
Schleiermacher teaches that the pure a priority of the 
Hegelian Dialectic and the pure ä posteriority of Empiricism 
are alike one-sided and untenable. He says,’ ‘= he judgments 
(together with the system of notions) which constitute science 
are developed in every individual identically, in proportion to 
the activity of his intellectual function, because of the relation 
between organic function and the outer world, which exists in 
all men.’ Schleiermacher, accordingly, traces all scientific 
judgments to the co-operation of an inner and an outer factor, 
which are equally necessary for the formation of any judgment 


in the sense given above. 
1 Dial. §§ 189-192. 


§ 74. Definition of Inference. 





PART FIFTH. 


INFERENCE IN ITS REFERENCE TO THE OBJECTIVE 
CONFORMABILITY TO LAW. 


§ 74. INFERENCE (ratio, ratiocinatio, ratiocinium, dis- 
cursus, συλλογισμός) in the widest sense is the deriva- 
tion of a judgment from any given elements. Deriva- 
tion from a single notion or from a single judgment is 
IMMEDIATE INFERENCE or (immediate) consequence (conse- 
quentia immediata). Derivation from at least two 
judgments is MEDIATE INFERENCE, or inference in the 
stricter sense (consequentia mediata). 


As the conception represents the individual existence and 
what is to be distinguished in it, and the notion represents the 
essence, so the judgment and inference represent the relations 
of single existences. The judgment has to do with the primary 
and nearest relations ; the simple judgment with a fundamental 
relation; and the complex judgment with a placing side by side 
of several relations. Inference has to do with such a repetition 
of similar or dissimilar relations as givesrise to a new reference. 
The possibility of the formation of inference, and of its objec- 
tive validity (as will be proved afterwards), rests upon the pre- 
supposition of a real interdependence of things conformably to 
law. This is to be said of mediate inference only, however, for 
immediate inference is a mere transformation of the subjective 
form of thought and expression (though not of the expression 
alone). 


Q 








TEE EI ν΄. OE 








226 § 74. Definition of Inference. 





- € To derive from’ means to accept because of —- else, 
so that the acceptation of the validity of the one depen s ἫΝ 
the acceptation of the validity of the other, 1.6. 18 rc 
therefore and in so far, because and in as far as the other 1s 


received. | 
The “ immediateness’ in the so-called ‘immediate inference 


is relative. It implies that this kind of ee a 
require, as mediate inference does, the addition μῆς ἘΠῚ 
datum to the first, but at once and of itself yields the oi 
judgment, which is nevertheless another Bene fi 
merely another verbal expression. There is no Imme ia ‘ ἣν 
in the full sense, that no activity of thought is required to reac : 
the derived judgment; but since the term 18 — τες αν 
holds good in ἃ relative sense, it 18 not advisable to c ro τ 
When a change in terminology 1s not absolutely essential, 1 
does harm, produces unintelligibility, and gives occasion to 
a Plato, συλλογίζεσθαι and συλλογισμός do not occur in the 
sense of later logical terminology. They have a wider and 
more indefinite meaning—to draw a result from several data, 
taking them all into consideration 5 and, more commonly—to 
ascertain the universal from the particular.’ Er 
Aristotle defines:? συλλογισμὸς δέ ἐστι λόγος, ἐν Φ τεθέντων 
τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει τῷ ταῦτα 
εἶνα. This definition is not meant by Aristotle to include 
immediate inference. It comprehends the two kinds into which 
mediate inference divides—inference from the universal to the 
particular, and inference from the particular to the universal. 
In this sense, Aristotle distinguishes between ὁ διὰ τοῦ μέσου 
συλλογισμός and ὁ διὰ Tis ἐπαγωγῆς; Or ὁ ἐξ ἐπαγωγῆς en 
γισμός.2Σ Syllogism, in the strict sense, 1s inference rn t e 
universal to the particular. Aristotle says, in this sense, τρό- 
πον τινὰ ἀντίκειται ἡ ἐπαγωγὴ τῷ συλλογισμῷῳ "---ἅπαντα πισ- 
τεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆ. ER 
Wolff, in agreement with Aristotle, and, like him, referring 


1 Theaet. 186 D; cf. Phileb. 41 c. 2 Anal. Pri. i. 1, 24, 18. 
3 Ibid. ii. 23. 4 Tbid. 


$ 74. Definition of Inference. 227 





to mediate inference only, defines it:! est ratiocinatio operatio 
mentis, qua ex duabus propositionibus terminum communem 
habentibus formatur tertia, combinando terminos in utraque 
diversos; syllogismus est oratio, qua ratiocinium (seu dis- 
cursus) distincte proponitur. 

Kant? defines inference to be the derivation of one judgment 
from another. This happens either without an intermediate 
judgment (iudicium intermedium), or with the help of such. 
On this is based the division of immediate and mediate 
inference. Kant calls the former inferences of the under- 
standing, and the latter inferences of the reason. 

Hegel? sees in inference the re-establishment of the notion in 
the judgment, the unity and truth of the notion and judgment, 
the simple identity into which the formal distinctions of the judg- 
ment have returned, the end and aim towards which the jude- 
ment in its various kinds advances gradually, the universal 
which by means of particularity has coalesced with individual- 
ity. He thinks inference the essential basis of all truth, the 
intellectual and all intellectual, the return upon itself of the 
mean of the moments of the notion of the actual. Hegel here 
also identifies the logical and metaphysical relation, or the 
form of knowledge and existence. 

Schleiermacher* defines inference to be the derivation of one 
judgment from another by means of a middle premise. He does 
not recognise inference to be an independent third form, 
co-ordinate with notion and judgment, and denies that it has a 
real correlate of its own. He therefore does not believe that 
it has any scientific value for the production of knowledge; 
but thinks its worth didactie only, for the transmission of 
knowledge already existing. We believe this view to be 
erroneous, and will seek to show ($ 101) the real correlative of 
inference, and its significance as a form of knowledge. 

[J. S. Mill’ defines inference to be the setting out from 
known truths to arrive at others really distinct. He refuses 
the name to the so-called ‘immediate inferences,’ because in 


' Log. §§ 50, 332. ? Kritik der r. Vern. p. 360; Log. ὃ 41 ff. 
* Log. ii. 118 ff; Eneycl. § 181. 4 Dial. p. 268. 5 [Log. i. 185. ] 


Q 2 











228 § 75. The Principles of Inference 27 general, 


them the progression from one truth to another 18 nied 
apparent, not real, the logical consequent being a mere 7 i- 
tion of the logical antecedent. He divides inference into three 
kinds, from generals to particulars, from particulars to = 
rals, and from particulars to particulars. The third = ; 
though not generally recognised by logicians, is not only valid, 
but is the foundation of both of the others. It is the inference 
of every-day life, and in its finer forms corresponds to = 
ἐθισμὸς of Aristotle, which plays such an important part in the 
formation of our judgments in matters of taste and morality— 
the delicate imperceptible ingathering of instances gradually 
settling and concreting into opinions. It is the recognition 
and discussion of this third kind of inference in all its manifold 
forms, but more especially in its formation of religious DE, 
which gives so much logical value to J. H. Newman s Grammar 


of Assent, 2nd ed., Lond. 1870. | 


- r xl S 
$ 75. The PRINCIPLES OF INFERENCE are the axiom 


of identity and correspondence, of contradictory disjunc- 
tion (or of Contradietion and Excluded Third) and of 
sufficient reason. The derivation of a judgment from a 
notion rests on the first, the derivation of a judgment 
from a judgment on the first and second, and the deri- 
vation of a judgment from several judgments on the 
first, second, and third. 


Logic considers these principles as rules of our thinking 
(which is also an act of knowing). It leaves to psychology to 
discuss in how far these laws are, or are not, so simple and 
evident in their application that they cannot be altered in clear 
thinking, and in this sense attain the character of natural laws 
for our thinking. 

Aristotle does not place these axioms at the head of Logic, 
but discusses them, in so far as he enunciates them in scientific 
form at all, partly and occasionally as laws of the formation 
of inferences, and partly and more particularly in the Meta- 


δ 75. The Principles of Inference in general, 229 





physics,' where he holds the axiom of Contradiction to be 
πασῶν βεβαιοτάτη ἀρχή. 

Leibniz? holds them to be the principles of our inferences 
(raisonnements); Wolff does as Aristotle. 

Daries and Reimarus were the first to find the principle of 
Logic in some or other of those axioms. Reimarus places? the 
essence of reason in the power to reflect upon conceived things 
according to the two rules of consistency and contradiction, and 
holds that by the right use of reason the knowledge of truth is 
to be attained. He defines the ‘ doctrine of Reason’ to be a 
science of the right use of reason in the knowledge of truth,‘ 
and truth in thinking to be the agreement of our thoughts with 
the things we think about.° He seeks to prove the proposi- 
tion, ‘ When we think according to these laws of consistency 
and contradiction, our thoughts must also correspond to the 
things themselves, and so be true ;’ “these laws are sufficient to 
give truth and correctness to all our thoughts.” 

Kant, on the other hand, reduces formal Logic to the doctrine 
of the laws which flow from the principles of Identity and Con- 
tradiction, in this sense, that by their observance the agree- 
ment of thought with itself, or the absence of contradiction, 
will be attained. He does not believe possible an agreement 
of the contents of thought with actual existence or with things 
in themselves. 

Fries remarks’ that these axioms should not be placed at 
the head of Logic, since they can only be understood in their 
true meaning when one has learned to know the notion and 
the relation of subject and predicate in the judgment. This 
remark is correct, for these axioms express the relation of 
several judgments to each other, and so have their first distinct 
influence upon the doctrine of inference. 

Delboeuf* places at the head of the whole of Logic three 
axioms which partly take the place of those given above. These 


1 Met. iv. 3. 2 Monad. § 31. 


Vernunftlehre, ὃ 15. 4 Ibid. § 3. 5 Ibid. § 17. 
Ibid. § 17 ff. 7 System der Logik, § 41. 
Log. pp. 91 sqq., 104 sqq., 118 sqq., and 130 sqq. 











το τε" ies RRR rel, Ree ne 


230 § 75. The Principles of Inference in general. 








axioms are—1l. We must conclude from the representation 
of phenomena to phenomena themselves; 2. We must posit 
the results as identical by abstraction of the differences; 
3. The logical concatenation of ideas corresponds to ng real 
concatenation of things. He derives them from ee first 
postulate of the reason ’_— “that certainty is possible,’ by the 
following argument. If certainty is to be given, truth must be 
given; if truth be given, our conceptions must be able to 
be true; if they can be true then—l. The mind must be able 
to conceive phenomena as they are. 2. The causes which 
produce them must remain identical with themselves in the 
various combinations into which they enter. 3. The logical 
power of deduction must also correspond to actual objective 
existence, the mental analysis be a true (though converse) 
pieture of the real synthesis. By means of the first principle 
we advance, says Delboeuf, from the conception to the actual 
existence, by means of the second from conceived identity to 
actual identity, by means of the third from conceived connec- 
tion to actual connection. Delboeuf finds the warrant for 
the agreement of a thought with what actually exists κε a 
thorough-going logical harmony ın the operations,—observ a- 
tion, conjecture, and verification (p. 85). Understood in this 
sense—that the agreement of thought with objective existence 
is attainable by man and guaranteed by the observation of 
the sum total of the logical laws (s. § 3)—the first of those 
three principles coincides with the principles of this system 
of Logic and of every Logic which is a doctrine of know- 
ledge. The second principle has chiefly to do with the process 
of abstraction (s. § 51). Delboeuf recognises the third principle 
to lie at the foundation of inferences (raisonnements) (cf. § 81). 
He calls these three principles ‘ prineipes reels, and makes the 
first two correspond to the prineiple of Identity, and the last to 
that of Sufficient Reason. He places beside them as ‘ principes 
formels’ the axioms of Contradiction and Excluded Third.’ 

[ Hamilton, Mansel, Thompson, and that school of formal 
logicians make Logic the science of these laws of thought and 


l Log. p- 165 ff. 


§ 76. The Axiom of Identity. 231 





their application. They push Kant’s doctrines to an extreme 
which he himself would have scarcely contemplated. But 
Hamilton, on the side of metaphysics, asserts that the three laws 
of Identity, Non-contradiction (as he calls it), and Excluded 
Middle are ‘ laws of things’ as well as ‘ laws of thought,’ and 
hold good of things-in-themselves.' They reject the law of 
Sufficient Reason because it either has to do with the matter, 
not the form of thought, or else is no law of thought, but 
only the statement that every act of thought must be governed 
by some law or other.” Mansel has tried to show how Logic 
should be merely a statement of these three fundamental laws 
—the laws of the thinkable—the deduction from them of the 
laws of thinking in the stricter sense—viz. those of concep- 
tion, judgment, and reasoning, and their thorough-going ap- 
plication to produce in thinking, consistency with itself. 

J. S. Mill refuses to place these laws at the head of Logic, 
and considers them of little or no value in the science. He 
severely criticises the views of Mansel and Hamilton in his 


Exam. of Sir Wm. Hamilton’s Phil.?] 


$ 76. The Axiom oF IDENTITY (principium identitatis) 
should be thus expressed: A is A, 1.6. everything 18 
what it is, or—omne subiectum est praedicatum sui. 
The axiom of consistency (principium convenientiae), 
which is allied with it, should be thus expressed: A 
which is B, is B; 1.6. every attribute which belongs to 
the subject-notion may serve as a predicate to the same. 
The reason of the truth of the axiom lies in this, that 
the attribute conceived in the content of the notion 


[' Cf. Lect. on Logic, i. 98. 


2 Cf. Mansel, Proleg. Log. p. 214, and Hamilton, Disc. 2nd ed., 
Appendix. 


3 Prolegomena Logica, 2nd ed. p. 190 ff. Cf. also Hamilton's 
Lect. ii. 244 for an elaborate list of authorities. 
4 Srd ed. pp. 480-480. ] 


nb. Rn lt A ION as »α. 








rn Be 





SES 


aia iether 
ee τ ττ 


ne ng ra 
{55 


a re 


a= & — nn ~ 
x = ς - 
τ Set ΞΟ Ως 


eS a ταος 
Fre 


e 





232 § 76. The Axiom of I denizly. 


inheres in the object conceived through the notion, and 
this relation of inherence is represented by the predicate. 
The sentence—Not-a is Not-A, is only an application 
of the axiom of Identity to a negative notion. It is not 
a new axiom. In the same way: A, which is Not-B, is 
Not-B, is only an application of the axiom of consistency. 
The latter formula furnishes a basis for the application 
of this thought to negative judgments in the axzom of 
negation (principium negationis)—A, which is not B, 
is not B. | 

In a wider sense the axiom of Identity may apply to 
the agreement of all knowledge with itself, as the 
(necessary though insufficient) condition of its agree- 
ment with,actual existence. 


The axiom of Identity was not, as some think, discovered by 
a Schoolman (perhaps the Scotist Antonius Andres, quoted 
by Polz, and after him by Bachmann and others, who enun- 
ciated the formula—ens est ens). Still less is it due to modern 
logicians. Parmenides, the Eleatic, is its author. He ex- 
presses it in its simplest form—éo7;' further, χρὴ τὸ λέγειν τε 
νοεῖν τ᾽" ἐὸν ἔμμεναι" oportet hoc dicere et cogitare: id quod 
sit, esse,? and ἔστι yap εἶναι" (cf. § 11). 

Heraclitus thought that anything is and is not, at the same 
time, and that all fleets. Parmenides thought that only Being 
exists; Not-Being is not; everything lasts. Plato seeks to 
overcome this opposition by his distinction between the in- 
variable world of Being or Ideas, whose every essence is always 
like to itself, tale, quale est, ἀεὶ κατὰ ταὐτὰ dv (Tim. p. 27, 
and elsewhere), and the changeable world of Becoming or of 
sensible things. Science or true knowledge has to do with 
existence, and consists in this, that what exists is known as 


1 Parm., Fragm. ed. Mullach, vs. 35, 58. 
2 Ibid. p. 49. 3 Ibid. 


§ 76. The Axiom of Identity. 


233 





existing'—ovxoby ἐπιστήμη μὲν ἐπὶ τῷ ὄντι πέφυκε γνῶναι os 
ἔστι τὸ ὄν :" ἐπιστήμη μὲν γέ που ἐπὶ τῷ ὄντι (πέφυκε) τὸ ὃν 
γνῶναι ws ἔχει."---λόγοο---ὃς ἂν τὰ ὄντα λέγῃ ws ἔστιν, ἀληθής, 
ὃς δ᾽ ἂν ὡς οὐκ ἔστι, ψευδής. The admission, that ἃ mere agree- 
ment of conceptions with each other is a criterion of their 
truth, is expressly rejected by Plato.‘ 

Aristotle defines® τὸ μὲν γὰρ λέγειν, τὸ ὃν μὴ εἶναι ἢ τὸ μὴ dv 
εἶναι, ψεῦδος" τὸ δὲ, τὸ ὃν εἶναι καὶ τὸ μὴ ὃν μὴ εἶναι, ἀληθές.5.-- 
ἀληθεύει μὲν ὁ τὸ διῃρημένον οἰόμενος διαιρεῖσθαι καὶ τὸ συγκείμενον 
συγκεῖσθαι" ἔψευσται δὲ ὁ ἐναντίως ἔχων ἢ τὰ πράγματα. When 
he’ requires from truth thorough-going agreement with itself— 
δεῖ yap πᾶν τὸ ἀληθὲς αὐτὸ ἑαυτῷ ὁμολογούμενον εἶναι, ravrn—this 
does not amount to the mere tautological oneness, which the 
axiom of Identity in its stricter sense requires, it also means 
the agreement of the consequences with the reasons.® 

Leibniz” enunciates as the first affirmative truth of reason, 
or as the first identical truth, the sentence ‘ everything is that 
which it is,’ or A is A. 

In a similar way Wolff’ considers the most universal iden- 
tical judgment to be the axiom—idem est illud ipsum ens, quod 
est, seu Omne A est A. 

The Wolffian Baumgarten" used the formula: omne pos- 
sibile A est A, seu quidquid est, illud est, seu omne subiectum 
est praedicatum sui, and calls this axiom “ principium positionis 
seu identitatis.’ 

Schelling'* declares the axiom inadmissible in scientific 
Logic, and very properly draws attention to this, that proposi- 
tions sounding identical do not belong, according to their sense, 
to the merely analytical principle, A is a. 

Hegel‘? makes the correct remark against the axiom of 
Identity in the form A is A, that no consciousness thinks, 


! Rep. v. 477 B. 


2 Ibid. p. 478 a. 3 Cf. Cratyl. 385 2. 
4 Ibid. p. 436. 


5 Metaph. iv. 7, § 2. 

δ Ibid. ix. 10, § 1. 7 Anal. Pri. i. 32; cf. Eth. Nicom. i. 8. 
® Cf. De Interpret. c. xi. 9 Nouv. Essais, iv. 2, § 1. 

'0 Log. ὃ 270. Il Metaph. $ 11, 1739. 

12 Phil. Schr. i. 407. 13 Log. 1. 2, 32 ff; Encycl. $ 115. 











234 § 76. The Axiom of Identity. 





eech 
nor conceives, nor speaks according to this ἫΝ a 
conducted according to it would be absurd:—A pla 
is— lanet. 
lant ; the planet is—the p | ὩΣ 
: Schleisrmacher' thinks that the axiom, In order en to n 
must either express the identity of the sub) 


r la . 
empty formula, \ of science, or the identity of thought and 


as the conditior 


existence as the form of MEHR: Lene 22 
: ; ‚cians? make 
Some more recent logı 


and self-identical nature of human rn an 
notional knowledge, and make the — [ τ “x er 
its negative form. But this is too far en a — τε 
ing and application which has been er ᾿ an 
Logic, and especially in the doctrine of in wee m. 
ie the time of Aristotle. The doctrine of the En 
also another metaphysical principle, ee = > 
whose sienificance is by no means ex | 
identity ‘with itself (ef. $ _ hg. reg en 
the axiom must contain the prıncıp 
ikon meaning must be given vr er nn = ar 
snow oener ‚le. 
a: = =, this postulate be signified 
0 by means of the adequate en ge Pr 
rather than concealed under the ambiguous ormula, = m. 
Delboeuf recognises the axiom of Identity, interpre nr 
by the postulate that every judgment be true, L.e. in an er 
with actual existence (which meaning was sete " bray ot 
edition of this work), or by the first or second ὁ 
‘incl . § 75). 

en ai nn ων that the law of Identity — 
the fact that every object of thought, as such, 18 ee Ἢ 
limitation and difference, as having definite . sips ne 
which it is marked off and distinguished from all others; g, 


1 Dial. § 112. 
2 nn Ueber die philos. Bedeutung des RT = or 
tät, in Fiehte’s Zeitschrift für Philosophie u. spec. T eol. π᾿ 
ey 1839: I. H. Fichte, De principiorum contradictionis, identi > 
gr oe in logicis dignitate et ordine dissertatio, pp. 10 ff., 26, 1849. 


exclusi te 


$77. The Axiom of Contradiction. 235 





in short, itself and no other; and that an object is in any other 
way inconceivable. It is the law of logical Affirmation and 
Definition." J. δ. Mill? expresses the law of Identity thus— 
“Whatever is true in one form of words is true in every other 
form of words which express the same meaning.’ He calls it 
an indispensable postulate in all thinking, and says that it is 


of value in Logic,—providing for (e.g.) the whole of Kant’s 
‘ Inferences of the Understanding.’] 


$ 77. The Axıom or(th&favoidance of) Cowtrapıc- 
TION (principium contradictionis) is—Judgments op- 
posed contradictorily to each other (as—a is B, and A is 
not B) cannot both be true. The one or the other must 
be false. From the truth of the one follows the false- 
hood of the other. The double answer, Yes and No, to 
one and the same question, in the same sense, is inad- 
missible. The proof of this axiom comes from the 


definitions of truth (§ 3), of the judgment (§ 67), and 


of affirmation and negation (§ 69). ccording to these 


definitions, the truth of the affirmation is equivalent to 
the agreement of the combination of conceptions with 
actual existence, and consequently to the falsehood of 
the negation. The truth of the negation is equivalent 
to the absence of agreement between the combination 
of conceptions and actual existence, and consequently 
with the falsehood of the affirmation. Hence, when the 
affirmation is true the negation is false, and when the 
negation is true the aflirmation is false—which was to 


_be proved. 


The axiom of Contradiction may be applied to an 


[! Cf. Mansel’s Proleg. Log. pp. 195-96, 2nd ed.; Hamilton’s Lect. 
on Log. i. 81. 


° Exam. of Sir Wm. Hamilton's Philos. 3rd ed. p. 466. ] 


LO ARETE vi 08 








236 § 77. The Axiom of Contradiction. 


- 





individual notion (notio contradictionem involvens sive 
implicans), to the combination of a notion with a single 
attribute (contradictio in adiecto), and further to the 
repugnance (repugnantia), i.e. to the mediate contra- 
diction which first appears by inference in corollaries, 
in so far as these forms can be resolved into two judg- 
ments opposed contradictorily to each other. 


Although the axiom of contradiction is so simple and obvious 
in itself, many questions and discussions have clustered round 
it in the course of the centuries during which it has been con- 
sidered to be the first principle in Logic and Metaphysics, 
and require to be strictly examined. These have to do chiefly 
with its expression and signification, its capability for proof, 
its validity, and the sphere of its application. 

Irs Exrressıon.— The formula most commonly used is,— 
Judgments opposed contradictorily cannot be true at the same 
time. This must be rejected as inexact. It leaves it uncertain 
whether the relation of time which lies in the ‘at the same 
time’ refers to the judgments themselves as acts of thought, 
or to their content. If the former (which the verbal sense of 
the formula implies), then, because of the relation of time, the 
law says too little. . It does not suffice for the avoidance of the 
contradiction that its one member is thought now, and the other 
then. Can it have been true in the eighteenth century that 
the works of Homer proceeded from one poet, while it is- true 
in the nineteenth that they have several authors? If, how- 
ever, the formula bears the second meaning — Judgments 
opposed contradictorily cannot both be true so far as their 
content has reference to one and the same time—then (1) the 

words of the formula strictly taken do not mention this, and the 
expression, which must be as strict as possible in formulas of 
this kind, suffers from grammatical inexactness, and (2) the law 
is burdened by a superfluous addition. One judgment which 
agrees with another in other things, but differs in the determi- 
nation of time (although this difference does not enter into the 


877. The Axiom of Contradiction. 237 








verbal expression, but only lies implicitly in the reference 
to the presence of the person who judges at a particular time) 
is no longer the same judgment. Hence its denial does sie 
make the contradictory opposite of the other judgment. Hence 
the law of Contradiction, which has only to do ah judgments 
contradictorily opposed, cannot be applied to judgments of that 
kind, and it is not necessary, in order to state this inapplica- 
bility, that the formula should contain a determination of time. 
The determination of time has no more right to admission than 
a determination of place, and than all other adverbial determina- 
tions, none of which require particular mention for the same rea- 
son, that judgments in which they differ cannot stand opposed 
to each other in contradictory opposition. If the “at the same 
time’ does not denote a relation of time (simul), but the being 
true together, or community of truth (una), it is better to avoid 
the double sense which has led so many not insignificant 
logicians astray by the expression,— They cannot both We true. 

Its Meantna.—Perfect sameness of sense, both in the 
single terms of the two judgments and in their affirmation and 
negation, is the condition without which no contradictory 
opposition can take place. Hence, in given judgments, which 
according to sound appear to be opposed contradictorily, the 
relation of thought is to be strictly tested in these references. 
MW hen judgments contradict each other in words only, and not 
In sense, or when they appear to be logical judgments, but 
are really, because of the indefiniteness of their sense, mere 
rudimentary thoughts, yes and no very often can, and must 
rightly, be answered to the same question. For example, it 
can be both affirmed and denied, without any real tal; 
tion existing between the answers apparently contradictorily 
opposed, that Logic is part of Psychology, if the word psycho- 
logy, in the affirmative answer, be used in its widest sense (as 
equivalent to mental science), and in the negative answer in 
a narrower sense (as, e.g. that given in § 6). The logical 
demand, that a choice be made between yes and no, ἌΡΕΣΕ 
in force after that the possibility of a simple answer has been 
established by the strict statement of the ambiguous sense of a 











238 § 77. The Axiom of Contradiction. 





question and the correction of its somewhat erroneous presup- 
positions. Not a few empty disputed questions, and not a few 
obstinate mistakes and deceptive sophisms, have been con- 


nected with the neglect of this precaution. 
The possibility of a different sense in the way in which the 


affirmation and negation is to be understood rests on this, that 
the combination of conceptions contained in the judgment may 
be compared, either with existence in the absolute sense or with 
the mere objective phenomenon (as it is conditioned by the 
normal function of the senses), and with this latter in various 
ways. For example, the question whether the sun moves on 
in space must be affirmed, denied, and again affirmed, as it 
refers to the first sensible phenomenon, to the system of the 
sun and the planets revolving round it (looked at from the 
distance of their centre from the centre of Gravity), or to the 
relation of the sun to the system of the fixed stars. Finally, he 
who (with Kant) believes that all existence in space is merely 
‘phenomenal, conditioned by the peculiar nature of man’s sense- 
intuition, and refers the question to the sun as ‘a thing-in- 
itself, or to the transcendental object, which, since it affects 
us, causes the appearance of the sun in space, must give a 
denial to the question, from this critical stand-point. 

Irs Proor.—The possibility and necessity of proving the 
axiom of Contradiction may be disputed, because it is a first 
principle, and so cannot be derived from another. At the most 
it can only be proved in the indirect way, that no thinker can 
avoid recognising its validity in any individual case. But it 
is doubtful whether this axiom is absolutely first and underiv- 
able. It has been often denied by Sceptics, Empiricists, 
and Dogmatists. And we ourselves believe that the highest 
logical principle is not the axiom of Contradiction, but rather 
the idea of truth, i.e. the consistency of the content of percep- 
tion and thinking with existence (cf. §§ 3, 6). The desirability 
of a proof can scarcely be denied now, when there are so many 
discussions of its correct formula, validity, presupposition, and 
the probable limits of its application. These can never find a 
settlement which will be generally recognised without some 


$ 77. The Axiom of Contradiction. 239 





proof which will make clear the true meaning of the axiom 
The fact that in some treatises the very truth of the axiom Ἔ 
seriously questioned contradicts in the most forcible way the 
vague assertion of its innateness, which would by anticipation 
prevent every philosophical investigation and recommend blind 
submission to the incomprehensible authority of the axiom 
The possibility of proof rests on sufficient definitions of wath: 
of the judgment, and of affirmation and negation. If these ‘es 
premised, then it is (as an analytically-formed proposition) 
deduced without difficulty from the mere analysis of the 
notions.. Accordingly, the proposition correctly bears the 
name of fundamental proposition (axiom) only in so far as it 
has a fundamental significance for a series of other propositions 
those, viz. in the doctrine of inference and proof, but not in 
the sense that it is itself underivable. j 

Several objections of course arise against the general possi- 
bility of proving the axioms of contradiction, and against the 
special deduction given above. The deduction, it may be said 
presupposes the validity of the axiom. To deduce it from the 
definitions is only possible on the presupposition that the 
contradictory cannot be true. But this objection proves too 
much or nothing at all. The same thing may be said of all 
logical laws—the thinking which deduces them rests upon 
them. If on this account demonstrations become fallacious 
reasonings in a circle, all scientific representation of Logic 
must be abandoned. | But it is not so. For though these 
laws carry with them their own validity, and they are (at first 
unconsciously to us) [actually ne = our actual thinking 
even in that which deduces them, yet this deduction does not 
rest upon a scientific knowledge of these laws; and this know- 
ledge is to be carefully distinguished from their actual validity | 
(cf. § 4). The deduction of the axiom of Contradiction, as of 
any other logical law, would be a reasoning in a circle, if 
the proposition to be proved is itself, explicitly or implicitly, 
presupposed as known, and .as one of the means of proof, as 
a premiss; but this does not happen in the above deduction. 
This fallacy does not occur because the thinking, which makes 




















240 877. The Axiom of Contradiction. 





the deduction, is correct, ie. by its being conformable to the 
law to be derived as well as to the other logical laws." 

It may be objected to our proof and to the validity of the 
axiom, that the deduction given above presupposes real existence 
to be the steady standard of thinking. This, however (one may 
say), can only happen upon the metaphysical presupposition i 
the unchangeable persistency of all actual existence. Under soe 
opposite metaphysical presupposition, and in reference to the 
objective phenomenal world, that very standard of — 
may be brought under the influence of time and become itsel 
changeable. And in this way the necessary truth of the 
axiom is destroyed, or at least narrowed to a very limited 
sphere. We do not accept the metaphysical presupposition, 
however, for we (§ 40) have recognised the reality of change 
in time independent of human comprehension. istory shows 
that most famous thinkers of the past and of the present, 
Parmenides and Herbart, and in a certain reference Plato 
himself and Aristotle, have held the validity of this logical 
principle to be connected jointly and separately with that of the 


metaphysical a and that, on the other hand, Heraclitus 


and Hegel, who contéde reality to Becoming and Change, also 


allow the axiom of Contradiction to disappear in the vortex of 
the universal flux: Nevertheless, we maintain our two theses 
equally firmly, Motion and Change have reality ; but this does 
not exclude the universal validity of the proposition that 
judgments opposed contradictorily to each other cannot both 
be true. The appearance that one of these theses excludes 


1 This conformability appears to me to exist only in the division of 
the possible relations of thought to actual existence, into agreement 
and want of agreement (cf. $ 69), on which division the above prooi 
rests (p. 235). This division is a dichotomy, because, in commnianteng 
the notions of Negation and Falsehood, we comprehend whatever is not 
agreement under one other notion. If we believed (as Delboeuf, Log. 
p- 61 ff. does) that the principle of Contradiction enters into the pre- 
misses of the proof given above, and that it is therefore not valid as 
an actual proof, the discussion would still have significance nana 
showing the relation of that principle to the fundamental definitions 


(and so Delboeuf accepts it). 


877. The Axiom of Contradiction. 241 





the other is due to that one-sided view of the judgment which 
sees in the subject and predicate its only essential constituent 
parts, while all the different parts of the proposition which 
grammar distinguishes have a logical significance, and cor- 
respond to just as many parts in the judgment (§ 68). The 
determination of time does not belong to the formula of the law, 
but to the judgments to which the law finds application, if these 
refer to something which belongs to a section of time. If 
the objective existence with which the judgment has to do is 
a changing one, it is postulated that the same change enters 
into the combination of conceptions, and that it may come into 
consciousness along with the contained element of time. To 
this section of time the conception generally must be referred, 
and the simple elements of the conception to those points of 
time which are within this section. In this way, in spite of 
the continuous change, the conception of what has happened 
finds its steady, i.e. sure, standard in what has actually hap- 
pened. An historical fact, e.g. the assassination of Caesar, 
belongs as a whole to a definite section of time, and in every 
moment during its occurrence must bear the character of that 
which continuously happens. Nevertheless, the law of truth, 
excluding the contradictory opposite, for the judgment which 
relates to it, is:—The judgment is true if the real motion in 
the occurrence is truly mirrored by the corresponding ideal 
motion in the combination of conceptions, so that our concep- 
tion of the occurrence takes its place in our conception of the 
universal connection of historical occurrences in our conscious- 
ness, just as the occurrence has its place in this connection in 
actual existence; and the conception of each of its elements is 
arranged in the conception of its whole course, as each element 
is arranged in the actual and real course of the event. His- 

torical judgments affirming and denying the same about an 

occurrence in time, e.g. Socrates was born 469 B.c., and 

Socrates was not born 469 B.c. (but 470 or 471), are as 

strictly opposed to each. other as contradictories, and can as 

little be both true as the mathematical judgments which refer 

to unchangeable existence—the sum of the angles of any rec- 


R 























242 877. The Axiom of Contradiction. 


tilineal triangle is, and is not, equal to two right ἔμ παν 
Hegel and Herbart assert that motion and change νὴ gen a 
selves contradictory, and Hegel teaches that motion is = 
existing contradiction. Every moment of passing ον jr ἫΝ 
the one circumstance into the other (e.g. the beginning © ay) 
unites in itself predicates which are opposed as contr: dictories 
to each other. Hegel asserts that these contradictory judg- 
ments are both true in reference to the same moment; but 
Herbart thinks that that is impossible according to the irre- 
fragable law of Contradiction, and that the passing over ἮΝ 
and the becoming another, have no reality.’ Both ea 
are false. The semblance of contradiction results from δι 
indefiniteness of the sénse, and disappears as soon as every 
individual expression is referred to distinet notions. >) 
means of striet definition of notions secure points of en 
are at once reached. For example, if the beginning of 4) 
be defined to be the moment in which the centre of the sun's 
disc appears above the horizon, the time of passing over into, 
which unites in itself the predicates opposed as contradictories, 
must now signify either a finite or an infinitely small rg 
of time, or none at all. If the first be the case, the parts ὁ 
the finite section of time lie either on the negative or on eu 
positive, or upon different sides of the boundary. In the er 
case (when the time of dawn is called the passing over of nig : 
into day, or the beginning of day), the negative rasch 
and it only, is true. The time of the passing over into, . t " 
beginning, in this sense, is not the present existence (the = n 
is not day). In the second case, when all parts lie on t 16 
positive side (when the first time after the passing over into 
is called the beginning of day), the affirmative judgment, and 
it only, is true. The beginning, in this sense, belongs to the 
time of present existence (to the day). In the third case, 
where the parts of the section of time, which forms the passing 
over into, fall on different sides (e.g. when the time between the 


1 Hegel, Wiss. der Logik, i. 2, p. 69, ed. 1834; cf. i. 1, p. 78 ff 
Encyel. ὃ 88, p. 106, 3rd ed. 1830; Herbart, Einl. in die Phil. ὃ 11% 
Metaph. ii. p. 301 ff. 


877. The Axiom of Contradiction. 





transit of the upper, and the transit of the under edge of the 
sun’s disc is considered as the time of passing over into, or 
as the beginning of day), the difference holds good of the 
different parts of the subject, and the two judgments now 
stand as co-ordinate to each other. The one part of the begin- 
ning in this sense belongs to the time of the present existence (to 
the day), and the other does not: But no contradiction exists 
in this any more than in the co-ordination in space of different 
attributes in one subject. With reference to the undivided 
subject, however, the negative judgment, and it alone, is 
true (the time of the passing over into, in this third sense, 
considered as a whole, is not a part of the day). This does 
not prevent it, that the affirmative judgment, and it alone, is 
true of one part of the subject. If an infinitely small section 
of time be taken to denote the passing over into and begin- 
ning of, it must either fall on the one side, or on the other 
side of the boundary point, or divide itself on either side. In 
all these three cases, however, and for the same reasons, there 
is no more contradiction than in the supposition that the 
passing over into and the beginning of, is denoted by a finite 
section of time. Lastly, no contradictory judgments arise 
under the third supposition, that the boundary point itself, 
without any reference to extension in time, denotes the pass- 
ing over into. For this boundary point is a nothing of 
time. Its extension in time is supposed to be equal to zero. 
There are, therefore, no positive predicates at all which can 
be predicated of it. In actuality, present existence is joined 
to non-existence immediately, i.e. without any intervening 
(finite or infinitely little) time. (For example, the ended 
transit of the centre of the sun’s disc through the horizon to 
the time anterior to the transit.) The boundary point, so far as 
it is represented as something existing, or as a real intervening 
time which is also a nothing of time, is a mere fiction, which 
for mathematical purposes cannot be dispensed with, but 
which is destroyed in logical reference by the contradiction 
which it bears in it.! If this non-existent be feigned to exist, 


! This fiction rests on the abstraction, which holds fast and modifies 


2 























244 $ 77. The Axiom of Contradiction. 
and be made the subject of a positive assertion (the point of 
time of the beginning belongs to the time of ne 
—the point of the beginning of day belongs to 2 2 
assertion is false, and what is opposed to it as contrac -_ = 
true; not in the sense that this feigned point of a a 
to the time of what is about to exist, but in the sense τ ‘ 
does not belong to time at all. It is no part of eg Ὁ ΜΕ 
finite nor infinitely little. It is a nothing of time. ἂν e ers 
say of this judgment what Aristotle said of the oo 
τραγέλεφός ἐστι λευκός. It is false, and its denia ; ; 
in the sense that the stag-goat had another colour, but mer 

there is no such existence, and its conception 15 a mere — 
We cannot, therefore, agree with Trendelenburg, who = 
that a contradiction is present in motion,' and yet mo t - 
motion has reality, because the axiom of contradiction, 7 ough 
of irrefragable validity within its own limits, _. e ἡ 
on, which only conditions and creates the objects to 





plied to moti 


which it applies.” The axiom of contradiction may be applied 
to the notion of motion 1 we do not confine our attention to the 


easy caret 
proposition which is without difficulty—* Motion - se = 
analyse the notion and go back to the elements which are - 
together in it, as Trendelenburg ‚himself has = in = 
süitemsente given above, that “motion ( why not rat = Pi 
which moves itself?) is and is not at the same point at the 


same time.’ According to our previous explanations, this 


the second of two really inseparable predicates—to N εν "ἢ 
occupy a place—while it completely sets aside the = 
nizian monadology, and the Herbartian assertion of simple a τὰ ” : 
involve the mistake of taking for real the separability o the 2 
predicates, which exist only in abstraction, and of hypostatising 
a ed. i. 187; 3rd ed. 1. 189: ‘ Motion, which μα = 
of its notion is and is not at the same point at the same se με = u 
contradiction of dead identity; ’ 2nd ed. i. 271; 3rd ed. 1. 27 ; 4 

int first carries that contradiction which was present in motion as 
soon as the elements contained in it were separated. 

2 Ibid. 2nd ed. ii. 154; 3rd ed. il. 175. 


S77. The Axiom of Contradiction. 245 





being and not being, at the same point at the same time, is a 
mere fiction. Motion is not impossible because it is not con- 
tradictory. 

Yet it would appear as if the axiom of Contradiction, at 
least in one special case, admits of an exception, which is not 
excluded, but confirmed by the above argument. The actual 
existence to which the judgment refers, and in which it finds 
its measure of truth, whether it be external or internal 
(mental, psychic), is in both cases generally opposed to the 
judgment itself as another thing. The truth of the Judgment 
depends upon it, but it, on its side, is not dependent upon the 
truth of the judgment. Now, there is one case in which the 
dependence is mutual. The actual existence to which it refers 
becomes another thing by the judgment (and that not me- 
diately by an action connected with the judgment, but imme- 
diately by the judgment become a thought). Hence the 
judgment appears able to become false because of its own truth. 
It is evident that this case happens when, and only when, the 
truth of the judgment is itself the object of the judgment, or 
belongs to the object of the judgment. The ancients have 
empirically discovered this case, without (so far as we 
know) giving an account of its logical nature. What is 
called ‘The Liar’ represents it. Epimenides, the Cretan, says, 
all the Cretans are liars (Κρῆτες del ψεῦσται). No logical 
difficulty exists if the invariable practice of lying refers only 
to the majority of cases, or rather to a prevailing inclination to 
lie; and this is the meaning of the sentence spoken by anyone 
who wishes to depict the Cretan character. It is also un- 
doubted that the assertion, if the invariable habit of lying be 
strictly understood, is actually false, and false only. It may 
be granted, however, that apart from this assertion of the 
Cretan Epimenides, the proposition— All Cretans are always 
in all things liars—is true in all cases without exception. 
This assertion, although actually inadmissible, contains nc 
internal contradiction, and in this sense is not impossible. But 
now it may be asked whether, on this presupposition, the 
axiom of contradiction has or has not validity when applied 











877. The Axiom of Contradiction. 





to the assertion of Epimenides, and whether this assertion, 
together with its contradictory opposite, can or cannot be 
true? Here is a logical problem which must be solved scien- 
tifically, and must not, as too commonly happens with modern 
logicians (the ancients, at least, tried earnestly to solve it), 
be evaded by one or other way of escape, least of all by an 
appeal to the pretended innateness and absolute character of the 
axiom. If,on the above presupposition, the assertion of Epime- 
nides universally comes to pass, and is true; then if a stranger 
had asserted it, its contradictory (Cretans are not always in all 
they say liars, but sometimes speak the truth) would be, and 
remain, false. But since Epimenides, who has made this true 
assertion about the Cretans, is himself a Cretan, there is this 
one true assertion spoken by a Cretan. Hence the proposition 
that Cretans always lie about everything has become false 
by its own truth; and its contradictory opposite is just as 
. true as itself, This may also be put thus:—If the general 
statement about the Cretans is true, it must also be true 
of Epimenides the Cretan, and of his assertion. He must 
in this statement have told a falsehood. The statement has 
proved itself false by its own truth, and its contradictory must 
be true. The two propositions then—This expression is true, 
and It is not true, are both true, contrary to the principle of 
contradiction. (Our first consideration had for its basis the 
truth of the assertion of Epimenides as its logical predicate. 
This must help to serve to constitute the objective matter of 
fact, and we infer from this matter of fact to its untruth in its 
content. The second proceeds from the meaning of the truth 
of the assertion in its content, and infers, back from it to a 
matter of fact to which it belongs, that the attribute to be 
untrue belongs to its assertion.) If we first take the expres- 
sion to be false, we find ourselves equally compelled to con- 
clude that it must also be true. For all other assertions of 
the Cretans, according to the above presupposition, are false- 
hoods. If this assertion of Epimenides be untrue, they are all 
absolutely untrue. But then, because of this matter of fact, 
the assertion is true that all Cretans are always liars; the pro- 


877. The Axiom of Contradiction. 247 





position has become true by its untruth. The same may be 
shown in the following way :—If the assertion is untrue that 
all Cretans are always liars, then, that at least one ΔᾺΣ 
ample must be given where a Cretan speaks the truth. But 
according to the above presupposition, all their other assertions 
are untrue, and the assertion of Epimenides cannot be untrue 
but must form a single exception, and be true; and so “ele 
given us the statement of its truth from its untruth. The 
propositions, This expression is not true, and It is true, are 
again both true. (In this statement, as in our previous one, 
our first consideration has for its basis the untruth of the 
assertion of Epimenides as its logical attribute. Let this now 
be taken along with the matter of fact, and from the matter 
of fact, the truth of the assertion, in its content, follows. ‘The 
second, on the other hand, proceeds from the meaning of the 
untruth of the statement in its content, and infers fom ἢ back 
Saige s.0 eat m de me ma νον. 
| ame ¢ on.) But yet, in 
spite of this apparent confirmation, it would be too hasty a 
decision to grant that there is here an actual exception to a 
axiom of Contradiction. Under the simple grammatical eG 
pression two different logical judgments are comprehended 
the second of which cannot at all be thought, nor can exist ie 
an actual judgment, unless the first has been previously 
thought. The first judgment has to do with all other ae 
tions of the Cretans. It is true, and only true, on the pre- 
supposition on which we have here gone, that they are all of 
them untrue. Its contradictory is false, and false only. The 
second can only be formed with reference to this first judg- 
ment. In the second a similarly sounding statement is made 
with such universality that it also refers to the first judgment 
and its truth. But since the true assertion lies in the first 
judgment, the proposition in this enlarged sense is not more 
generally true, but false, and false only. Its denial or con- 
tradictory is true, and true only. If that complete strictness 
of thought and of expression of thought prevails, without which 
all these investigations are useless, we cannot assert that the 














248 877. The Axiom of Contradiction. 


same judgment, by the truth belonging to it, may change the 
. matter of fact with which it has to do, and thereby become 
false. We must correct our statement in this way—By the 
truth of the first judgment the second becomes false, whose 
ideal presupposition is formed by the first. Hence the axiom 
of contradiction, in spite of this very deceptive appearance of 
an exception, asserts its exceptionless validity. 

To absolutely shun contradiction is a task demanding so 
harmonious a thorough construction of thought, and at the 
same time such a purity and freedom of intention, that to fulfil 
it remains an ideal which is ever to be reached proximately 
only. Not merely gaps in our investigation, but every kind of 
ethical narrowmindedness, the tenacity of national, religious, 
political, and social prejudices, lead to contradictions. The 
difficulty of overcoming contradictions reveals itself in anti- 


thetic propositions. Cf. § 136. 
Irs History.'—We make the following remarks on the 


history of the axiom. 

Parmenides, the Eleatic, placed the positive axiom, ἔστιν, OF 
ἐὸν ἔμμεναι, or ἔστι yap εἶναι. by the side of the negative, οὐκ 
ἔστι μὴ Eval,” Or, οὔτε γὰρ οὐκ ἐὸν ἔστι,3 or, οὐ γὰρ φατὸν οὐδὲ 
νοητόν ἐστιν ὅπως οὐκ ἔστι," Or, οὐ γὰρ μήποτε τοῦτό γ᾽ ἔῃ 
(φανῇ ?) εἶναι μὴ ἐόντα." In these expressions, and especially in 
the last,® lies the germ of the axiom of Contradiction. They 
decline to assert that, what is, is not; and they deny the co- 
existence of the truth of the judgments—This is and This is 
not.” These expressions in Parmenides, however, have rather 
a metaphysical than a logical meaning. 


1 Cf. the Articles of Weisse and I. H. Fichte referred to in § 76. 

2. Parm. Fragm. ed. Mullach. vs. 35. 

3 Vs. 106. 4 Vs. 64-69. 5 Vs. 52. 

6 The forms given above partly depend upon conjectures in the 
(Plat.?) Sophist. p. 237. Bergk supposes τοῦτ᾽ ov Aay ἦ; cf. my Hist. 
of Philos., translated by G. S. Morris, New York, 1871 (4th Germ. ed. 
1871), i. § 19. 

7 The axiom did not originate, as Weisse thinks, in the opposition 
of Aristotle to the Stoics, nor yet, as I. H. Fichte (cf. as above ,p. 17 


supposes, in the Platonic Doctrine of Ideas. 


u 


$ 77. The Axiom of Contradiction. 249 








| Socrates says:! Os ἂν βουλόμενος τἀληθῆ λέγειν μηδέποτε τὰ 

αὐτὰ περὶ τῶν αὐτῶν λέγῃ, ἀλλ᾽ ὁδόν τε φράζων τὴν αὐτὴν τοτὲ 
‘ ς τὰ κου 

"ἫΝ ἕω, τοτὲ δὲ πρὸς ἑσπέραν palm, . . . δῆλος ὅτι οὐκ 

Plato, when he is engaged with the metaphysical problem of 
establishing the relation between Being and Becoming, distin- 
guishes intelligible and sensible things. Every BR thing 
unitesin itself the oppositions,—what is large is at the same Pie 
little, what is beautiful is at the same time ugly, &c. We πε 
not establish the thought that it is what it is, nor yet that it 
may be the opposite, or is not, for all sensible things are in 
continual change. Hence, they have not existence ah vacil- 
late between existence and non-existence: ἅμα ὄν 3 καὶ ᾿ ὄν 
-- ἐκεῖνο τὸ ἀμφοτέρων μετέχον τοῦ εἶναί τε καὶ μὴ εἶναι. On ds 
other hand, the axiom of Parmenides about Beine is true of 
the Idea. It is ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχουσα. πε: the Phaedo 
Plato mentions, besides ideas and sensible things, a third il 
viz. the qualities which inhere in sensible ds He are 
does not attribute persistent sameness to ideas only but asserts 
of the qualities of sensible things also, that they, so eee a 
remain that which they are, can never become nor be at the 
same time the opposite: od μόνον αὐτὸ τὸ μέγεθος οὐδέποτ᾽ 
ἐθέλειν ἅμα μέγα καὶ σμικρὸν εἶναι, ἀλλὰ καὶ τὸ ἐν ἡμῖν μέγεθ 
οὐδέποτε προσδέχεσθαι τὸ σμικρὸν οὐδ᾽ ἐθέλειν a a 
Suche TO ἕτερον, ἢ φεύγειν Kal ee δον νιν οὐκ 
ἐθέλει----οὐδὲν τῶν ἐναντίων ἔτι ὃν ὅπερ Hv ἅμα τοὐναντίον «γύγνε 
σθαί τε καὶ εἶναι αὐτὸ τὸ ἐναντίον ἑαυτᾷ ἐναντίον οὐκ agin 
γένοιτο; οὔτε τὸ ἐν ἡμῖν, οὔτε τὸ ἐν τῇ φύσει.“ PRES a 
ἄρα---μηδέποτε ἐναντίον ἑαυτῷ τὸ ἐναντίον ἔσεσθαι. Plato αὐ rs 
of sensible things, however, the opposite always comes Sica ὦ 
opposite, and that opposite qualities are in them at the same 
time :’ οὑτωσὶ γίγνεται πάντα, οὐκ ἄλλοθεν ἢ ἐκ τῶν ἐναντίω 
τὰ ἐναντία. ἐκ τοῦ ἐναντίου πράγματος τὸ ἐναντίον ἀῶ, 


In Xenophon Memorab. iv. 2, 21. 
Plat. de Rep. v. 478 sqq. 

Ibid. p. 102 εΕ. 
Ibid. Ρ. 70 pb. 


3 Phaedon, p. 102 ». 
5 Ibid. p. 103 Β. © Ibid. p. 103 c. 
8 Ibid. Ρ. 103 ». 





fo OD en - τ -" 


m ie near ττι 


ὧδ τ τ. 








th 2 eet? 








77. The Axiom of 


yiyveodaı.! ἄρ᾽ οὐ---λέγειϑ τότ᾽ εἶναι ἐν τῷ Zi ee ον 
μέγεθος καὶ σμικρότητα ; ἔγωγε. Cf. the words in an : ge 
quoted passage of the Rep. p. 479 B: ἀνάγκη eae ae a 
αὐτὰ αἰσχρὰ φανῆναι καὶ ὅσα ἄλλα ἐρωτᾷε"---ἀεὶ ἕκαστον. rn 
τέρων ἕξεται. In another passage Ὄ οὐκοῦν — = το ® 
ἅμα περὶ ταὐτὰ ἐναντία δοξάζειν ἀδύνατον εἶναι ;—from w 1 . 
sure, &c. 
is proved that the λογιστικὸν whose ἔργον it is to measure, Sc. 
is different from the lower parts of the mind : τὸ. ae τὰ 
μέτρα ἄρα δοξάζον τῆς ψυχῆς τῷ κατὰ τὰ μέτρα οὐκ ἂν εἴη ταὐτὸν 
__the union of different parts of the contradiction in the object 
is not taken into consideration, but the existence of the contra- 
diction in the thinking subject is. This copious quotation 1s 


needed to make clear in how far it is an incorrect —. 
to say (as is often done) that Plato has enunciated the axiom 0 
Contradiction (particularly in the words,’ μηδέποτε ἐναντίον 
ἑαυτῷ τὸ ἐναντίον ἔσεσθαι). The axiom of Contradiction has 
‚to do with contradictory opposition exclusively ; the passage 
quoted from the Phaedo refers, in the first instance at least, to 


predicates opposed as contraries. The difference between “el 
trary and Contradictory Opposition was not enunciate 7 
Plato with the distinctness which is eg —_ 0 

the pure apprehension of the axiom. Thus he believes st 
when he finds contraries combined in things, he must ascribe 
to them Contradictory Opposition. The change of predicate 
—the same thing has now, and then has not now, the same 
predicate—seems to him rather a contradiction in things. 
(The thought that, because the second point of time is 
another one, and therefore the second judgment in the affirm- 
ative a new judgment, and its negative form not the contradic- 
torv of the first, would have solved the difficulty, but lies beyond 
Platonism.) Accordingly, Plato excludes sensible things from 
the domain of this axiom (in both senses) because they are, 
what is and at the same time is not. He places under ıts 
authority the εἰλικρινῶς ov, that which is uniform ee, 
changeable-—Ideas and Mathematical objects. The axiom least 


1 Phaedon, p. 102 B. 2 Plat. Rep. 603 a. 


3 Phaedon, p. 103 c. 





δ. 77. The Axiom of Contradiction. 251 





entangled in ideological relations, and approaching most closely 
to the logical form in Aristotle, is stated in the Euthydemus,' 
where it is said to be impossible that any existing thing may 
not be what it is (ri τῶν ὄντων τοῦτο, ὃ τυγχάνει ὄν, αὐτὸ τοῦτο 
μὴ εἶναι). 

Aristotle, developing Plato’s doctrines, expresses the axiom 
of Contradiction as a metaphysical axiom in the following care- 
fully circumscribed formula,—It is impossible that the same 
can and cannot belong to the same in the same reference : 3 τὸ 
αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ 
καὶ κατὰ τὸ αὐτό.) Ina parallel passage‘ he makes the ex- 
pression of contemporaneousness ἐν τῷ αὐτῷ χρόνῳ co-ordinate 
with the ἅμα οὕτω καὶ οὐχ οὕτως. By adding to the signi- 
ficance of the ταὐτό, Aristotle expresses the same axiom in 
the shorter formula,—The same cannot be and not be: τὸ 

| Ὁ ὦν = \ ᾽ “. Ἰδύ 6 > / e a4 

avTo ἅμα εἰναι TE καὶ οὐκ εἶναι---ἀδύνατον. ἀδύνατον ἅμα εἶναι 
καὶ μὴ εἶναι. Aristotle joins to this the corresponding logical 
axiom,—It is not to be asserted that the same is and is not; 
Contradictory expressions cannot both be true :® βεβαιοτάτη 
δόξα πασῶν τὸ μὴ εἶναι ἀληθεῖς ἅμα τὰς ἀντικειμένας φάσει».ϑ 
10 4 \ > / > , θ e \ a} > “~ 10 > 

ἀδύνατον τὴν ἀντίφασιν ἀληθεύεσθαι ἅμα κατὰ τοῦ avTod.'© ἀντι- 

[4 > @/ eo > m 9 11 u | > [4 
paceis—ovy οἷον TE ἅμα ἀληθεῖς εἶναι. Cf." καὶ ἔστω ἀντίφα- 
σις τοῦτο" κατάφασις καὶ ἀπόφασις αἱ ἀντικείμεναι.) μὴ ἐνδέ- 

Ψ / \ > / 13 LOU e a . ἡ 
χέσθαι ἅμα φάναι καὶ amobavan.! ἀδύνατον ὁντινοῦν ταὐτὸν 
ὑπολαμβάνειν εἶναι καὶ μὴ εἶναι. We can recognise the influence 
of the Platonic thought in Aristotle’s statement, that nothing 
can be true if all things are in motion; and that in order 


: P, 298 », 2 Metaph. iv. 3, § 13 Schw. 

ὅ The statement of the axiom reminds us of the passage quoted in 
another sense from Plato, Rep. iv. 436: δῆλον, ὅτι ταὐτὸν τἀναντία 
ποιεῖν ἢ πάσχειν κατὰ ταὐτὸν γε καὶ πρὸς ταὐτὸν οὐκ ἐθελήσει ἅμα. 

* In the Metaphysics, iv. ὅ, § 39. 5 Anal. Pri. ii. 2, 53 B, 15. 

6 Metaph. iii. 2, § 12. 7 Cf. Ibid. iv. 4, § 1. 

8 Ibid. iv. 6, ὃ 12. 9 Ibid. § 13. 10 Tbid. p. 8, § 3. 

'U De Interpr. p.6. 13 Anal. Post.i.11. 13. Metaph. iv. 3, § 14. 

14 Metaph. iv. 8, § 10: εἰ δὲ πάντα κινεῖται, οὐθὲν ἔσται ἀληθές, πάντα 
ἄρα ψευδῆ: cf. iv. 5, ὃ 27, and ix. 10, § 4. 











252 877. The Axiom of Contradiction. 
to completely secure the validity of the axiom of Contra- 
diction, Aristotle thinks he must state that there is an exist- 
ence unchangeable throughout.’ But he does not, like Plato, 
hold the axiom to be absolutely invalid with reference to the 
changeable. By means of his distinction between δύναμις 
and ἐντελέχεια or ἐνέργεια, he more correctly shows that the 
same object may at the same time possess the capacity or 
possibility for opposites, but cannot contain the opposites in 
actuality or in their developed existence :? δυιάμει ἐνδέχεται 
ἅμα ταὐτὸ εἶναι τὰ ἐναντία, ἐντελεχείᾳ δ᾽ οὔ. This last pro- 
position, however, has to do with contraries rather than with 
contradictories. Besides, Aristotle does not hold the axiom of 
Contradiction (as modern Formal Logic does) to be a sufficient 
foundation for a whole logical system. So far from this, he 
makes mention of it only occasionally in his logical writings, 
and considers it to be a principle of Demonstration only; and 
this not without the distinction that the axiom of Excluded 
Middle has a more intimate connection with indirect than the 
axiom of Contradiction has with direct Demonstration.’ 
Aristotle sought to deduce the logical form of the axiom 
from the metaphysical (by a course of reasoning which is not 
stringently correct) ;° and, conversely, from the supposed truth 
of the logical to prove the truth of the metaphysical.® He 
thus placed the two in the strictest reciprocal relation. But 
he explains that it is impossible to deduce its truth from a 
higher principle by direct proof, for the reason that the axiom 
(in its metaphysical form) is itself the highest and most certain 
of all principles:7 φύσει γὰρ ἀρχὴ καὶ τῶν ἄλλων ἀξιωμάτων 
αὕτη (ἡ «δόξα) πάντων. βεβαιοτάτηδ αὕτη τῶν ἀρχῶν πασῶν. 
The validity of the axiom itself can only be proved indirectly, 
viz. by showing that no one can help recognising it in actual 
thinking and acting, and that were it destroyed all distinctions 
of thought and existence would perish with it.? According to 


2 Ibid. iv. 5, § 9. 

4 Anal. Post.i.11. ° Metaph. iv. 3, § 13. 
7 Ibid. iv. 3, § 16. 
9 Tbid. iv. 4. 


Metaph. v. §§ 10, 33. 

Cf. Ibid. ix. 9, § 2. 

Ibid. iv. 6, $$ 13-14. 
" Ibid. p. 4, § 2. 





S77. The Axiom of Contradiction. 25 





the statements we have given above, a direct proof is impossible 
only when distinct definitions are wanting. The proof of the 
axiom in its metaphysical form may be put thus:—If the 
thought, or whatever is defined to be a copy (picture) of actual 
existence, differs from its real original, then the notions of 
untruth and non-existence find application, conformably to the 
definitions enunciated above. The notion of untruth is to be 
referred to the supposed image or picture. The notion of Exist- 
ing-but-not-in-this-manner is applied to what the copy was 
defined to correspond to; and the notion of Non-Existence is 
applied to what was falsely thought to be the real correlate 
to the elements which do not agree with it. Truth and 
falsehood, like affirmation and negation, are only in the image 
in so far as the image can be referred to the thing, and ave 
in the domain of actual existence only in so far as images 
exist in it. The notion of the Existence exists independently 
of that of the image (while, on the other hand, the notion 
of reality implies that the existence has become known by 
means of an act of thought different from it, and may be applied 
to thinking itself, only in so far as this thinking has itself 
become the object of thought to another act of thinking reflect- 
ing upon it). Non-Existence is neither in the image (although 
it may be in its denial) nor in the object (although the exist- 
ence of the object in a judgment, which is therefore false, may 
be denied), but simply does not exist. The notion of non- 
existence, however, is primarily in the negative judgment in 
which we think the discrepancy between image and actuality. 
It can always be used to denote what does not exist, but is 
falsely conceived to exist; never to denote what does exist. 
In other words—It is not true, that the same thing which is, 
also is not; or (as Aristotle says)—It is impossible that the 
same thing is and also is not.’ 
The Aristotelian doctrine, in spite of many attacks, remains 
the prevailing one in antiquity, in the middle ages, and in 
modern times. 


1 Cf. Trendelenburg, Log. Unters. ii. § 11: Die Verneinung. 





254 Contradiction. 


In Antiquity.—The axiom of Contradiction was attacked by 
the Sceptics, who believed that the one of the two contradictory 
opposites was not truer (οὐδὲν μᾶλλον), or at least not more able 
to be proved true, than the other. Epicurus also attacked it. He 
did not wish to abolish it absolutely, but only to make it as 
indefinite as some things themselves are. The bat (vurrepis), &-g. 
is a bird and yet is not a bird. The stem of the broom (vap@n€) 
is and yet is not wood, &c.' (Plato had said the same thing in 
reference to the world of sense.) But this exception is false. 
In such intermediate forms, which according to the notions of 
natural science do not belong to a definite class, the negative, 
and this only, is true. If a more extended notion is enunciated 
which includes it, then the affirmative is true. But then the 
judgment (in spite of the identity of words) has materially 
become another, and this affirmation is not the contradictory of 
the former negation. 

In the Middle Ages.—The Thomists followed Aristotle un- 
conditionally ; but in the School of the Scotists, doubt began 
to attack, not the axiom itself, which Aristotle, the highest 
authority in philosophical matters, had declared to be most 
certain, but its outworks. The question was raised, whether 
the axiom had the originality of a highest principle. The 
Scotist Antonius Andreae appears to have been the first who 
denied its originality and the impossibility of its direct proof. 
He sought to derive the axiom of Contradiction from the axiom 
ens est ens, which he thought was the positive and earlier. 
Somewhat later the Thomist Suarez defended the Aristotelian 
doctrine, and discussed the formula, ens est ens, in order to 
show that it could not, because of its emptiness and barrenness, 
be the highest principle and ground of metaphysies.° 

In Modern Times. — The axiom hasexperienced bolder attacks. 
Locke* despised it as a meaningless abstraction, an artificial 


1 Ioann. Sic. schol. ad. Hermog. vi. 201, ed. Walz, republished by 
Prantl, Gesch. der Log. i. 360; cf. Cie. De Nat. Deorum, i. 25. 
2 De Rep. v. 479. 3 Cf. Polz, Comm. Metaph. pp. 13, 21, 61 sq4- 


4 Essay, iv.7. 


877. The Axiom of Contradiction. 255 





construction of the Schools yielding no food for actual thought 
But the reputation of the axiom was more firmly stahl 
after that Leibniz undertook to vindicate it, and combated 
Locke’s objections. Leibniz held it to be an innate piinoiple 
which does not arise from experience, and indispensable as ὰ 
rule for scientific knowledge.'! He says,? that on the strength of 
this principle we hold to be false what contains a contradiction 
and believe to be true what is opposed as its contradictor ' 
to what is false. The last case, however (though Leibniz 
did not recognise it) presupposed that PER BE may be 
known to be false in another way than by an internal con- 
tradiction. Every contradiction must be represented in the 
form of two judgments which are opposed to each other as 
contradictories, the one or other of which is necessarily false. 
3ut we cannot know, merely by means of the axiom of Con- 
tradiction, which of the two is false. We only know, accord- 
ing to this axiom, that it is false that both are true. But to 
this falsehood nothing is opposed as its contradictory save the 
axiom—The two members which a contradiction contains in 
itself are not both true. The axiom «is correct enough, but 
does not teach us how to find out which of the two ER 
is the true one; and this is the problem. It is only when we 
know in some other way the falsehood of a definite one of the 
two members, that the axiom, that the contradictory opposite 
of the false is true, satisfies the demands of our knowledge and 
comes to have a real value. ᾿ 
Wolf, like Aristotle, considers the metaphysical axiom to 
be self-evident,—fieri non potest, ut idem praedicatum eidem 
subiecto sub eadem determinatione una conveniat et non con- 
veniat, immo repugnet,? or: si A est A, fieri non potest, ut 
simul A non sit A;4 and deduces from it, by means of the 
definition of Contrary and Contradictory Opposition, the 
logical axiom of truth and falsehood,—duae propositiones con- 
trariae non possunt esse simul verae;° propositionum contra- 


Nouv. Essais, iv. 2, § 1. 2 Monadol. ὃ 31. 
Ibid. § 271. 5 Ibid. ὃ 529. 


3 Log. § 529. 








256 $77. The Axiom of Contradiction. 


dictoriarum —-altera necessario falsa.! Wolff also followed 
Aristotle in not considering the axiom of Contradiction to be 
the one principle of the whole of Logic (although he bases his 
Ontology upon it), and in mentioning it only occasionally in 
Logic. 

Baumgarten says, in his Metaphysic :? nihil est A et non-A: 
haec propositio dicitur principium contradictionis et absolute 
primum. 

Reimarus? formularises the law of Contradiction (prineipium 
Contradictionis) thus, —A thing cannot be, and at the same 
time not be. 

Kant‘ considers the axiom of Contradiction to be the principle 
of Analytic judgments. It is sufficient to establish their truth, 
and it furnishes a universal, though negative, criterion of all 
truth; for contradiction completely does away with and abolishes 
all knowledge. In Synthetic knowledge, according to Kant, it 
is inadmissible to act contrary to this inviolable principle ; but it 
‘3 no test of the truth of a synthetic judgment. It is the conditio 
sine qua non, but not the ground of the determination of the 
truth of our synthetic knowledge ; for even if a cognition be 
not self-contradictory, it may yet be contradictory to its object. 
Kant defines the expression of the axiom therefore— A pre- 
dicate does not belong to a thing which contradicts it. He 
rejects the Aristotelian-Wolffian formula,—It is impossible 
that something is and is not—partly because apodictic certainty, 
which should be understood from the axiom itself, is super- 
fluously brought in (in the word im possible), partly, and more 

particularly, because the axiom is affected by the condition of 
time. It is a merely logical axiom, and its expression must not 
be limited to the relation of time (or rather, the notion of con- 
tradictory opposite already includes identity of relation of time 
in the two members, so far as a reference to time exists in the 
case under consideration). Kant comprehends the axiom of 
Identity and the axiom of Contradiction under the common 


1 Log: ὃ 532. 2 Metaph. § 7. 3 Vernunftlehre, § 14. 
4 Krit. der r. Vern. p. 190 ff.; cf. p. 83 ff. 


8 77. The Axtom of Contradiction. 257 





designation, Axiom of Contradiction and Identity.‘ Those who 
have worked at Formal Logic since Kant generally share his 
views about the axiom of Contradiction, but think differentl 
of its relation to the axiom of Identity. Some seek to re 
the latter from the former, or the former from the latter; while 
others consider each to be a separate and independent schen. 
The question only amounts to how each of these axioms is to 
be taken. According to different ways of expression and 
comprehension they are to be considered either the positive and 
negative form of one and the same law, or two different laws 

Fichte? believes the axioms of Identity and Contradiction μ᾿ 
be the basis of our knowledge of the primary activity of the 
Ego (positing itself and the Non-Ego): and finds this action 
of the Ego to be the real basis of these axioms. 

Hegel? expresses the axiom of Contradiction in this way—A 
cannot be A and at the same time not be a. He considers it 
to be the negative form of the axiom of Identity, according to 
which A=A, or everything is identical with itself. He therefore 
thinks that this axiom, instead of being a true law of thought 
is only the law of the reflective or ‘ abstract’ undoes: 
The form of the proposition itself contradicts it. A a 
promises a distinction between subject and predicate, but this 
law does not perform what its form demands. It is, more- 
over, invalidated by the following so-called laws of thought 
(the axiom of Difference, the axiom of Opposition or of Ex- 
cluded Third, and the axiom of the Reason). The truth of 
these laws is the unity of the identity and the difference 
which finds its expression in the Category of the Renin: 
Thought as understanding lets things stand in their strict deter- 
minateness and distinction from others: its next higher stage 
Is the self-elevation of those finite determinations and their 
passing over into their opposites, wherein lies their Dialectic or 
negative-intellectual moment. Lastly, the highest stage is the 


' Logik, ed. by Jiische, p. 75. 

Grundlage der Wissenschaftslehre, p. 17 ff. 

| Logik, i. 2, p. 36 ff.; 57 ff; Zneyel. § 115; cf. 119 and 
§§ 79-82: ‘a kann nicht zugleich A und nicht A sein.’ 


5 











. 


258 $77. The Axiom of Contradiction. 














unity of the determinations in their opposition, the ._— 
or positively-intellectual moment, in which both the dua ism © 
the understanding and the one-sided monism of the er 
power of the reason reach their right position as the ce y 
dependent elements of free speculative truth. These Hegelian 
doctrines are not without truth (cf. § 80) in reference to con- 
trary opposites; but their transference to the relation of > 
tradietory opposition is based, as Trendelenburg has = Ἢ 
his ‘ Logische Untersuchungen,’ so clearly that we need only 
refer to his work in this place, upon the substitution of real 
opposition for logical negation. ; Chalybäus, too, says,’ ‘it 
must be granted that in the Hegelian system it would be se 
correct to say opposite instead of contradiction.’ Cf. § 31 anc 
§ 83, on the dialectic method ; ὃ 42, on the recognition of the 
gradation of things as the true mean between the two extremes, 
which lie in the dualistic or ‘ abstract-understanding : separa- 
tion, and the monistic or ‘ negative-rational ’ identification ; and 
also the deduction of the law of excluded middle m the next 
paragraph. As regards Hegel’s charge, that the axiom of 
Contradiction does not pay attention to the difference of predi- 
cate from subject, this has to do only with the form of u. 
selected by him to express it, which 80 far from being essentia 
to it is rather an expression very unsuitable and deviating from 
the true meaning. The true expression pays attention to pre- 
dicate and subject, and to every relation of the judgment. 
Herbart? reduces the axiom of Contradiction to the formula 
__< What is opposed is not one and the same.’ He not merely 
asserts the, validity of the axiom, but exaggerates its 
cance. He makes it exclude not merely the possibility 0 
uniting contradictory oppesites, or the affirmation and Ἂν 
tion of the same, but also the possibility of uniting ee 
and of uniting a mere plurality of predicates in the = - 
ject (unless it is an aggregate without true unity), and thet # 
fore the impossibility of thinking a thing with several changıng 


ı Die hist. Entwickelung der speculativen Philosophie von Kant bis 
Hegel, 2nd ed. p. 321; English translation by Edersheim, p. 419. 
Lehrbuch zur Einl. in die Philos. $ 39. 








877. The Axiom of Contradiction. 259 





qualities. Both extremes, the Hegelian and the Herbartian, 
are only expressions, from different sides, of the same funda- 
mental error—the substitution of contradictory and contrary 
opposition. Hegel transfers what is true of the latter to the 
former; Herbart, what is true of the former to the latter. 

[ Hamilton‘ thus states the axiom of Contradiction, or, as he 
calls it (after Krug), Non-Contradiction — What is contradictory 
is unthinkable. The logical import of the law lies in this, that 
it is the principle of all logical negation and distinction, and 
that it, together with the law of identity, regulates the cate- 
gorical syllogism. He does not make it, as some other formal 
logicians do, the only primary law of Logic; but makes the 
law of Identity and the law of Contradiction co-ordinate and 
reciprocally relative, and says that neither can be educed as 
second from the other as first. In every such attempt at deri- 
vation the supposed secondary is always necessarily presupposed. 
The two are, in fact, one and the same law, differing only by a 
positive and negative expression.’ 

Boole,’ in his attempt to reduce all logical to mathematical 
relations, to explain every possible operation and combination 
of thoughts by mathematical principles, and express them in 
mathematical notation, asserts, as his Fourth Proposition— 
‘ That the axiom of Metaphysicians which is termed the prin- 
ciple of contradiction, and which affirms that it is impossible 
for any being to possess a quality, and at the same time not to 
possess it, is a consequence of the fundamental law of thought, 
whose expression is, 2?=x.’ He proves his proposition very 
simply and elegantly from his mathematical premisses, but can- 
not be said either to have explained or derived the logical law. 
To prove his whole theory, as well as this particular part of it, 
Boole must show that the fundamental mathematical relations 

are (1) simpler, and also (2) of more extensive application than 
the logical. If this be shown, then he may go on to show that 


[! Lect. on Logic, i. 81-2; cf. Mansel’s Proleg. Log. p. 195 ff. 

? For a list of authorities upon this law of Contradiction cf. ib. 
li, 246. 

* Laws of Thought, p. 49. 








260 § 78. The Axiom of Excluded Third or Middle 





the less simple relations of Logic, which have a narrower 
sphere of application, may be reduced to those of mathematics, 
and Logic become part of the latter science. But in fact the 
mathematical relations which Boole assumes (e.g.) to prove the 
law of contradiction are neither more simple nor of more 
extensive application than the logical axiom proved by them." 

J. S. Mill? says that the law of Contradiction is a principle 
of reasoning in the sense that it is the generalization of a 
mental act which is of continual occurrence, and which cannot 
be dispensed with in reasoning. He would express the law 
thus—The affirmation of an assertion and the denial of its con- 
tradictory are logical equivalents, which it is allowable and 
indispensable to make use of as mutually controvertible. 

A. Bain? makes the law of Contradiction, with those of 
Identity and Excluded Middle, take rank among the maxims 
by which we attain consistency in thinking. Consistency re- 
quires that when we affirm a definite fact, we do not at the 
same time deny it; having made an assertion, we are to abide 
by that. As by the law of Relativity everything that may be 
thought of, and every affirmation that can be made, has an 
opposite notion or affirmation, thoroughgoing consistency re- 
quires that we must be prepared to deny the counter notion or 
affirmation. The maxim of consistency which provides for this 
is the law of Contradiction. | 


§ 78. THe Axiom or ExcLUDED THIRD or MIDDLE 
(principium exclusi tertii sive medu inter duo contra- 
dictoria) is thus stated: Judgments opposed as contra- 
dictories (such as Ais B, and A is not B) can neither 
both be false nor can admit the truth of a third or 
middle judgment, but the one or other must be true, 

1 Cf. the whole of Chapters II. (of signs and their laws) and III. 


(Derivation of the laws of the symbols of Logic from the laws of the 


human mind), pp. 26-51. 
2 Examin. of Sir W. Hamilton’s Philos. 3rd ed. p. 471. 


3 Deductive Logic, p. 16. ] 


between two Fudgments opposed as Contradictories. 261 








and the truth of the one follows from the falsehood of 
the other. Or,—The double answer, yes and no, can- 
not be given to one and the same question understood 
in the same sense. The validity of this law also follows 
from the definitions of truth (§ 3), judgment (ἢ 67), and 
affirmation and negation (ὃ 69). These definitions assert, 
that the falsehood of the affirmation is equivalent to the 
want of agreement between the combination of concep- 
tions and the reality it represents, and consequently 
to the truth of the negation; and that the falsehood 
of the negation is equivalent to the agreement of the 
combination of conceptions with the reality it represents, 
and consequently to the truth of the affirmation. 


The remarks made under the law of Contradiction upon the 
entrance of a determination of time into the notion of contra- 
dictory opposition, and the other references to the distinctness 
of the sense in the judgments, to the possibility of proving the 
axiom, to its presuppositions, and to the case of apparent 
exception, are all applicable to the law of Excluded Middle. 
They are, indeed, to be more carefully attended to because 
this law is even more liable to be misunderstood. 

Various objections, partly against the value, partly against the 
truth of the law, are founded upon false ideas of its aim and 
meaning. 

The vALveE of the law has been denied. It has been said to 
be devoid of meaning and to be superfluous. (The attacks 
have been made from the mutually opposite stand-points of the 
purely Speculative and of the Empirical Philosophy.) Its 
legitimate existence in Logic has been denied. It does not 
distinguish, it is said, between cases where the denial is proper, 
and those where it is not proper. It does not distinguish 
between partial and total negation. It is, consequently, 
a meaningless and barren formula! But the strength of 


' Hegel’s Encycl. § 119; Beneke’s Logik, i. 104 ff. 





262 ὃ 78. The Axiom of Excluded Third or Middle 





these objections lies in this, that they demand from the axiom 
what does not belong”to it. The axiom, rightly understood, 
does not say that we may search after predicates of any given 
subject by a sort of ‘mounting to the sky,’ and then find it 
able to be defined either by the positive notion or its contra- 
dictory opposite. It does not say that in order to know the 
predicates of Spirit, e.g., we may and do bring forward the 
notions of the qualities green and not-green, wooden and not- 
wooden, &c., and then rejoice in the certainty that in every case 
the one predicate must be applicable if the other is not. This 
would be absurd. The axiom presupposes a suitable question. 
It does not show what question is suitable. That follows from 
the essence of affirmation and negation (ὃ 69). There must 
be a motive for the affirmation. And usually the genus-notion, 
to which the predicate is subordinate, already belongs to the sub- 
ject. If the question be unsuitable, the axiom of Excluded 
Third gives an unsuitable, but not a false, judgment. (It is not 


false that Spirit is not blue, nor that a table does not think, 


&c. ; indeed, while the craze of table-turning and spirit-rapping 
lasts, this latter judgment is not even unsuitable.) The axiom 
is valid, without exception, in every case in which the question 
is distinctly unequivocal ; and therefore is not to be limited by 
annexing any condition which will embody the demands made 
above.! The axiom itself has nothing to do with its unsuitable 
application. It must be admitted, however, that the misinter- 
pretation of the axiom has been apparently sanctioned by the 
name which some logicians have given to the axiom of Excluded 
Third, and by the formula in which it is expressed. It has been 
called the ‘ Axiom of the determinability of every object by 
every predicate ;’ and has been expressed in the formula-—The 
one of all possible pairs of contradictory predicates must belong 
to every object. 

The application of the axiom in indirect proof shows that it is 
not valueless. The scientific postulate of systematic complete- 
ness demands that it be placed as the essential complement of 


1 As I. H. Fichte, De Prine. Contrad. dc. p. 30, and Ulrici, 
Logik, p. 125, demand. 


between two Fudgments opposed as Contradictories. 263 





the axiom of contradiction; and would demand the same in 
cases where it could not be applied. 

The TRUTH of the law has been denied. Objections are 
directed not merely against the value and productiveness of 
the axiom of Excluded Third, but also against its truth. Some 
logicians have limited it by certain exceptions. Others would 
entirely abolish it. The former think that the axiom is not 
valid when the subject is a general notion. For example, the 
triangle in general is neither rectangular nor not-rectangular.' 
But it is only the indefiniteness of the sense which causes the 
appearance of invalidity. If the sense of the sentence be— 
Every triangle is rectangular, the negation, and it only, is 
true. If the sense be—There are right-angled triangles 
which are objects of mathematics, the affirmation, and it only, 
is true. 

Others refuse to acknowledge the validity of the axiom at 
all.2 The mean between the contradictory predicates, they 
say, is often the true predicate. All development rests on 
the union of opposites. Between ‘ guilty’ and “ not-guilty’ 
there is ‘ not-proven.’ Between full imputation and no im- 
putation there is partial imputation. It would be a dangerous 
error to exclude this third case. It would often give judges 
the painful alternative of unjust acquittal or unjust condemna- 
tion, and give effect to expressions of only half truth in 
spite of better knowledge and desire. Absolute recognition 
or rejection, the simple division of the character into good 
and evil, leaving out of consideration all the intermediate 
grades, the partition of systems into true and false without 
making allowance for the gradual advance of knowledge, the 
separation of statements into credible or incredible and 
forged without including the myth or poetic truth,—all denote 
a certain crudeness of thought. The cultivated man knows 
how to recognise the finer ramifications of truth and error, 
and to draw the elements of truth, scattered everywhere, from 
under the coverings of error, as gold is drawn from dross. 


1 Krug, Denklehre, § 19, teaches this. 
2 Hegel and his school, and Fr. Fischer, Logik, p. 40 ff. 











264 ὃ 78. The Axiom of Excluded Third or Middle 





Hegel says, ‘a philosophy of history has to seek a moment of 
spiritual truth in the most languishing constitutions.’ Aris- 
totle? and, more distinctly, Leibniz? speak of elements of truth 
lying hidden in systems the most different and contradictory 
to each other, which the careful glance of him who searches 
most deeply may everywhere recognise. Leibniz‘ remarks (in 
opposition to Bayle) that the reason, when it recognises two 
views opposed to each other to be both false, thereby promises 
a deeper insight. But neither Aristotle nor Leibniz have 
explained themselves more definitely upon the relation of that 
relativity to the absolute validity of the logical laws of Con- 
tradiction and Excluded Middle, which is recognised by both 
philosophers. The opposition is established by later philoso- 
phers. ‘If the knowledge of truth is not comprehended in 
a development,’ Erdmann says, in Hegel’s sense,° * everything 
is either wholly truth or wholly not-truth. Truth becoming, 
or developing itself, is both or neither the one nor the other.’ 
‘The strict maintenance of the laws of Identity and Excluded 
Middle, principles of the ‘ heathen Aristotle,’ is even explained, 
humorously, but with all earnestness, to be unchristian,’ 


because the reconciliation of opposites is the fundamental 


thought of Christianity (guilt removed, a ‘felix culpa’), while 
the persistency in opposition is heathenish. These observa- 
tions, however correct in themselves, and worthy of atten- 
tion, so far as they are to be considered as warnings against a 
false apprehension and application of the axiom of Excluded 
Third, prove nothing against the validity of the axiom rightly 
understood. They can only be held to be exceptions to it by 
exchanging contradictory for contrary opposition. Whoever’ 


1 Philos. der Geschichte, ed. of 1837, p. 202. 
2 Metaph. i. 10; οὗ ii. 1. 
3 In his third letter to Remond de Montmort, p. 704 of Erdmann’s 


edition. 
4 De Conform. fid. et rat. ὃ 80. 


5 Gesch. der neueren Philos. i. 2, 171. 
6 Fichte’s Zeitschrift für Phil. &c. xxviii. pp. 8, 9, 1856. 
7 Like Fr. Fischer, Logik, p. 40 ff. 


between two Fudgments opposed as Contradictories. 265 





first explains that by Non-a he means something else than 
other logicians do, viz. contrary, and not as they do, contra- 
dictory opposition, and then upbraids them with the incorrect- 
ness of their axiom because it does not hold good under his 
terminology, acts no way differently from the man who, first 
of all explaining that he deviates from Euclid’s usage, and 
understands, or at least comprehends, under ‘triangle’ the 
spherical triangle, then turns round and blames Euclid because 
he teaches that the sum of the angles of a triangle are always 
equal to two right angles. The stricture, however, is to a 
certain degree legitimate when opposed to the formula—A 
notion or its opposite is to be predicated of every object. But 
if one keeps strictly to the notion of contradictory opposi- 
tion, its opposing members denote only the presence or absence 
of a strict agreement of the combination of conceptions with 
the actual existence they represent. No one can really and at 
bottom doubt but that one of these two members must always 
be true, and that the axiom of Excluded Middle, which only 
asserts this universally, is true also. It is already implicitly 
given in the definitions of truth and falsehood, and affirmation 
and negation. According to these definitions, to explain the 
negation to be false, is equivalent to the denial of the want 
of agreement with what actually exists, and equivalent to the 
affirmation of the truth of the affirmation. To explain the 
affirmation to be false, is equivalent to denying the presence 
of agreement with what actually exists; and this is again 
equivalent to the recognition of the truth of the negation. 
The negation cannot be interchangeable with the affirma- 
tion of the predicate opposed as a contrary. Not guilty 
1s not equivalent to guiltless or pure. Not mortal (which 
may be said of a stone) is not equivalent to immortal or 
eternal, Not good (‘no one is good but God’) is not equiva- 
lent to .bad or wicked (the new-born child is not morally 
good. It requires education and the growth of personality in 
order to become good. But this is not to say that it is mo- 
rally bad); and so in all like cases. The truth of the nega- 
ion, which excludes the agreement of the positive statement 








266 § 78. The Axiom of Excluded T: hird or Middle 








with actual existence, does not exclude any degree whatever 
of approximation to this agreement. The question—Is this 
criminal guilty of this distinct crime ?—must be denied if 
only partial blame can be attached to him; because in this 
case the presupposition of blame conformable to the actual 
state represented does not occur. But the denial of this 
question does not make further questions, whether there 
has been any, and if so, what degree of approximation to full 
guilt, superfluous. It rather makes them necessary. The con- 
tradictory disjunction, guilty or not guilty, is not to be charged 
with the error of denying the possibility of half guilt or 
partial insanity. The error lies in making reciprocal the 
negation of this definite guilt with the affirmation of perfect 
innocence. The denial of guilt, as the accusation puts 1, 
leaves open the possibility of a certain degree of guilt. In the 
same way the negation of a full ability to manage one’s own 
affairs is always true, when its affirmation is false; but this 
‘negation is not equivalent to the assertion of complete incapa- 
city to manage one’s own affairs. Forms of transition between 
different kinds of the same genus are a mean between exist- 
ences positively distinct. They do not stand to each other 
in the relation of Being and N ot-Being, but in that of Being 
so and Being otherwise. Such transitions are not excluded 
by the law of Excluded Third between the affirmation and 
negation of the same. Grey is not a mean between white and 
not white, but between white and black; and belongs as well 
as black to not-white. The partially good character is not a 
mean between good and not good, but between good and bad ; 
and belongs to the not-good character. A gradual development 
in knowledge and a gradual approximation to perfect truth are 
not excluded by this axiom. Partial views which are opposed 
to each other as contrary opposites, are generally both false; 
but are not without an element of truth, for they both diverge 
from truth on the two opposite sides. In cases of this kind the 
application of the law of Excluded Middle requires much care. 
It is so very easy to confuse judgments whose predicates are 
contradictions, with judgments whose predicates are contraries ; 


between two Fudgments opposed as Contradictories. 267 





so very easy to make the negation, which should denote only 
the want of a strict agreement in everything or the presence 


of some divergence, denote a full divergence. This is more 


especially the case when practical motives get mixed up with 
the discussion. ‘The negation then both leads on those who 
frame the judgments to a full divergence on all points, and is 
so interpreted by others. When the one party combats the 
conclusion, the denial appears to be inseparable from the con- 
trary. In such relations, when the practical interest is con- 
sidered, he who is mentally free from the party errors which 
both sides fall under may be induced, in accordance with Solon’s 
law, to accept the partial error which is supportable, or at least 
rest content with not opposing it. He will thus avoid the iso- 
lation of negation, and will not give up the kernel with the 
shell, the thought with its inadequate expression. It is a 
logical duty, however, in theoretical reference, to make clear 
to one’s self and to those who seek the truth for its own sake, 
the falsehood of both extremes, and instead of the simple yes or 
no, to seek that construction of notion and judgment which 
makes possible a statement of the question more conformable 
to the state of the case. Dr. Richarz says forcibly,’ ‘ The im- 
possibility of answering certain categorical questions, about 
health or sickness, capacity for managing one’s own affairs and 
the want of such capacity, categorically, by a short yes or no, 
is often made matter of reproach against the science of medi- 
cine, and given as a sign of the inferiority of its stand-point. 
This is often done by jurists, who always require for their 
decisions concise expressions of the relations of circumstances. 
But most unjustly ; for, while he who investigates nature pro- 
ceeds on his course, and as his circle of vision widens he 
abundantly discovers new and wider conditions and relations in 
phenomena and notions which have hitherto seemed only simply 
related, which the plain affirmation and negation given to 
questions arising from the practical wants of life, are no longer 
sufficient to express.’ (It is with sanity and insanity as with 


! In the writing Reiner Stockhausen, mit Gutachten von M. Jacobi, 
F, W. Böcker, ©. Hertz, Fr. Richarz, Elberfeld, 1855, p. 131 ff. 


En EB nn EEE 








lt nen 
ungern 


ZI 3 


— „m ---  - -ο-“ο-ε:--.------ς- 








268 § 78. The Axiom of Excluded Third or Middle 





being of age and being under age; observation from the stand- 
point of natural science and instruction finds a gradual deve- 
lopment. Practical necessity first imposes strict limits, which 
are to be defined only according to laws imposed by jurists.) 
In the questions about „Homer, the adherence to extreme 
views marks the starting-point of investigation. A maturer 
scientific treatment seeks to investigate, not whether, but 
how far, the poems are to be referred to one or to more 
authors. A modern philologist says, ‘ People should at length 
cease to settle the Homeric question by a yes or no.’! The 
question— Was Thales a theist? cannot be affirmed; but 
neither can it be denied in the sense that he was an atheist. 
His stand-point lies without and is below the opposition of 
the clearly defined pure Theism or Atheism. The same is to 
be said to the question—Did he subscribe to the mechanical or 
dynamical theories of natural philosophy? The statement that 
Socrates was an upholder of the old morality and ancient 
simple faith of his people, must be denied; so must the asser- 
tion that he was a partaker in the philosophical movement to 
which the Sophists belonged. His stand-point was already 
above these two opposites. It was the higher point in which 
they became one. His old accusers made the legitimate denial 
of the first statement the ground for affirming the second ; and 
not a few ancient and modern defenders have made the legiti- 
mate denial of the second the ground for affirming the first. 
Both were led astray in different ways by the same misappre- 
hension—a misapprehension which finds easy entrance, and is 
inevitable, so long as the peculiarity of the higher stand-point 
is not recognised. In the naive sayings of children and of 
persons of kindly feeling, who are not accustomed to put things 
to the test of objective fact, there is often truth. They 
express their actual subjective feelings. But the concep- 
tions in which this truth is embodied do not strictly agree with 
the external actual fact. Now if the truth of these assertions 
be enquired after, and if the answer be limited to yes or no, 
the axiom of Excluded Third appears to justify this procedure ; 


1 G. Curtius in the Zeitschrift für die östr. Gymn. p. 115, 1854. 


between two Fudgments opposed as Contradictories. 269 











and does indeed justify it in so far as the negation is understood 
in the purely logical sense that a complete correspondence 
with fact in every particular does not exist. But it does not 
justify the negation in so far as it means a complete divergence 
from fact. It very often happens in this reference, that it is 
more difficult to formulate the question than to give the 
answer. In criminal cases the answer, guilty or not guilty, is 
left to the jury, but the statement of the question is entrusted 
to well-trained judges. A philosophical system may be partly 
true, when it contains true judgments along with false, and 
also when every individual judgment may approach more or 
less nearly to truth. And if a similar character pervades the 
whole system in strict connection, the very kind and degree of 
approximation to truth which exists in the principles of the 
system may be found in every individual proposition. The 
different systems which have appeared in the course of history 
may, in this sense, be looked upon as different stages in the 
development of human knowledge, and as degrees of approxi- 
mation to perfect knowledge. He who now-a-days, in presence 
of this historical development of scientific notions, can put 
questions such as the following—Is the human soul free or is it 
not? Is freedom a true good or is it not? Do the New 
Testament writings contain the whole of the Christian Revela- 
tion or do they not? Has the idea of philosophy embodied 
itself in Plato, or has it not? and the like ;—he who puts such 
questions, and demands a simple yes or no as answer, only 
proves that he has never studied the problems in hand, at 
least fundamentally. If he had, he would have first asked— 
What is freedom? What is revelation? What is truth? 
&c. In what sense and measure does the affirmation hold 
good, and in what sense and measure the negation? The 
conceptions, which exist before the scientific investigation, can- 
not be here presupposed to be self-evident. It is not their 
objective validity only that must be put to proof. In the form 
which they have before investigation, they are not absolutely 
valid, nor are they absolutely invalid. The chief task consists 
ın finding the truly valid notion. This task does not indeed 














270 § 78. The Axiom of Excluded Third or Middle 





promise ease. Thinking must strain itself to the highest 
degree possible. That restless bustle of action, which, with a 
ready yes or no, will proceed to external action, to stablish or 
revolutionise, but never will shake itself free of the bonds of 
those hurtful opposites, is not attainable by it. The true 
freedom of the mind is the stipulated reward of a disinterested 
resignation to pure thinking. Every false repose on a super- 
ficial affirmation or negation must be decidedly opposed. But 
we must hold as decidedly by the persuasion that there may be 
pure truth, in whose attainment the gradual succession of 
approximations find their end and aim, which finds its fulfilment 
in adequate science ; for then only the question rightly stated, 
which has already included the determinations which correspond 
to the facts, can be answered by yes or no. In its limited 
province, mathematics has almost thoroughly reached this end 
(and natural science has in great part). Its development re- 
_ quires only upbuilding, never or seldom rebuilding. It is fool- 
ish to explain this excellence to be a defect in mathematics; 
saying that it is a subordinate science, in which the laws of the 
reflective understanding yet hold good. The attainment of 
pure truth was an easier task for mathematics, because of the 
simpler nature of its problems, than it is to philosophy and to 
several of the other sciences. All, however, each in its sphere, 
are destined to reach the same goal by a gradual advance.' 

History OF THE Axıom.—As the logical consciousness 
of the axiom of Contradiction was developed by Parmenides, 
in his polemic against the common affirmation of contradictory 
opposites by Heraclitus, so the origin of the doctrine of the 
Excluded Third is apparent in Aristotle’s opposition to the 
Platonic assertion of a Third or mean between Being and Not- 
Being. 

Plato set on one side Ideas, as that which is, on the opposite 
side, matter, as that which zs not (but nevertheless made it the 


1 [This thought runs through the late Prof. Grote’s Exploratıo 
Philosophica. Professor Grote had, apparently, in a quite independent 
way, reached many of the conclusions of those modern German phi- 
losophers who are supporters of the Ideal-Realismus. ] 


between two Fudgments opposed as Contradictories. 271 





substratum of sensible things), and between the two as the 
Third, sensible things. They are, he said, an indefinite mani- 
fold, and are in continuous becoming and change. As such, 
they neither truly are, nor yet are not. Their true place 
must be considered to be the mean between Being and Not- 
Being :! καὶ yap ταῦτα ἐπαμφοτερίζειν, καὶ οὔτ᾽ εἶναι οὔτε μὴ 
εἶναι οὐδὲν αὐτῶν δυνατὸν παγίως νοῆσαι οὔτ᾽ ἀμφότερα οὔτ᾽ 
οὐδέτερον. ἔχει5 οὖν---ὅποι θήσεις καλλίω θέσιν τῆς μεταξὺ 
οὐσίας τε καὶ τοῦ μὴ εἶναι; 

Aristotle, on the other hand, allowed no mean between the 
members of the contradiction, between Being and Not-Being :? 
ἀλλὰ μὴν οὐδὲ μεταξὺ ἀντιφάσεως“ ἐνδέχεται εἶναι οὐθέν.3 ἀνάγκη 
τῆς ἀντιφάσεως θάτερον εἶναι μόριον ἀληθές----ἀδύνατον ἀμφότερα 
ψευδῆ εἶναι. Cf.4 ἀντίφασις δὲ ἀντίθεσις, ἧς οὐκ ἔστι μεταξὺ 
καθ᾽ αὑτήν. The assertion of a mean term, Aristotle thinks, 
would lead to the absurd consequence that Existence would 
be one-and-a-half-ply, made up of the Being and the half- 
Being which is between it and not-Being. Then between 
these two another mean must be taken, and so on ad infinitum. 
ἔτι εἰς ἄπειρον βαδιεῖται καὶ ov μόνον ἡμιόλια τὰ ὄντα ἔσται ἀλλὰ 
πλείω. Wolff teaches, like Aristotle®—inter contradictoria 
non dari medium;’ propositionum contradictoriarum altera 
necessario vera.® 

Baumgarten uses the formula®,—omne possibile aut est A aut 
non A, seu omni subiecto ex omnibus praedicatis contradic- 
toriis alterutrum convenit—a formula which is liable to the 
misapprehension stated above, that it authorises a universal 
comparison of any possible subject-notion with any possible 
predicate-notion. 


1 Rep. 479 c. 

* Analyt. post. i. 2. 

7 Log. § 532. 

® It is singular, since these words of Wolff are only a translation of 
the Aristotelian, that some think, such as Bachmann, Log. p. 62, that 
the axiom of Excluded Third is first found as principle of science 
in modern times and in Wolff. 

9 Metaph. § 10. 


2 Metaph. iv.7, § 1. 
5 Metaph. iv. 7, ὃ 9. 


3 Ibid. §§ 5-6. 
6 Ontolog. ὃ 52. 

















272 ὃ 78. The Axiom of Excluded Third or Middle 





Kant' explains the axiom, which elsewhere he incorrectly 
calls the axiom of Excluding Third, to be the basis of the 
logical necessity in apodictic judgments; but does not deter- 
mine the formula more closely. 

Kiesewetter, following Kant, says,—‘ The one or other of 
two attributes, contradictory to each other, must necessarily 
belong to every logical object.’ (The necessity lies only in 
the choice which must not be refused. The axicm does not 
teach at all, still less with apodictic certainty, which of the 
two members of the contradictory opposition is to be chosen. 
Hence the apprehension of the axiom, as a principle of apodictic 
judgments, rests on a misunderstanding. ) 

Krug,? who disputes the possibility of applying the axiom in 
its common form to genus-notions,? chooses the formula,—‘ Of 
opposed determinations of one thing you can only affirm one, 
and if you have affirmed this one you must deny the other’ 
‚— which is rather a formula for the axiom of Contradiction ; 
and ‘ Every possible attribute must either belong or must not 
to every object thought as thoroughly determined ;’ in which 
formula both axioms are comprehended. Krug calls this 
axiom the principle of reciprocal capacity for determination. 

Fries* uses the formulae,—‘ A notion or its opposite belongs 
to every object.’—“ Any notion belongs either affirmatively or 
negatively to any thing.’ He chooses the name,—Axiom of 
the determinability of any object by any predicate. The mis- 
apprehension of the axiom, already contained in Baumgarten’s 
formula, is still more provoked by this. 

Hegel's strictures® are justifiable against such a false appre- 
hension of the axiom, but not against the axiom itself. He 
says, ‘Difference in itself gives the axiom,—Everything is 
essentially different; or as it is also expressed,—Of two con- 
tradictory attributes only the one belongs to anything, and 
there is no third.’ (This is, however, not strict enough. The 
definition, only one predicate and not the two together belongs 


I Logik, p. 75. 
2 Denklehre, ὃ 19. Following Polz, Comment. Metaph. p. 107 sqq- 
3Cf£.p.263. 4 Log.$41l. 5 Ibid. i. 2, 66 ff.; Encyel. $ 119. 


between two Fudgments opposed as Contradictories. 273 





to the same object, has rather to do with the axiom of Contra- 
diction. The axiom of Excluded Third, on the other hand, 
says—ın every case the one predicate, and not both of the two, 
belongs to the same object, and Hegel himself recognises this." 
He calls the axiom in that form—the axiom of the opposite, or 
of opposition, or the axiom of Excluded Third. He thinks 
that this axiom contradicts the axiom of Identity. He combats 
it more especially by the assertion, that there is always a third 
between+A and—A, viz. A in its absolute value; and o is a 
Third between + and —. But here Hegel identifies the 
logical relations with the mathematical, from which, in spite of 
some similarity, they are to be essentially distinguished. Con- 
trary not Contradictory opposition exists? between positive and 
negative size in the mathematical sense. The negative quan- 
tity — A is by no means identical with the logical denial of + a. 
A quantity need not be either =+a or =—a. It may be 
either = + A or not = +, and also either = —A or not =—A. 
And looked at apart from the signs, according to its absolute 
value, it may be either =A or not =A. 

Herbart and his school rightly hold firmly by the validity 
of the axiom of Excluded Middle.? 

[ Hamilton‘ gives the formula— Of contradictory attributions 
we can only affirm the one of a thing; and if one be explicitly 
affirmed the other is denied. A either is or is not B.’ This law 
differs from the Laws of Identity and Contradiction by warrant- 
ing the conclusion from the falsehood of one contradictory 
proposition to the truth of another. Its logical significance 


I Logik, i. 2, p. 67. 

* Kant noticed this in his Versuch, den Begriff der negativen Grössen 
in die Weltweisheit einzuführen, 1763; Sämmtliche Werke, ed. by 
Hartenstein, ii. 69 ff. 

® Herbart, Z. z. Einl. in die Phil. § 39; Commentatio de principio 
logico exclusi medii inter contradictoria non negligendo, Gotting. 1833 ; 
cf. Hartenstein, Diss. de methodo philosophica logicae legibus adstrin- 


| genda, finibus non terminanda, Lips. 1885; Drobisch, Logik, 2nd ed. 


§ 57, 3rd ed. § 60. 
* [Lectures on Logic, i. 83. 

















274 ὃ 78. Axiom of Excluded Third or Middle, etc. 





lies in this, that it limits the sphere of the thinkable in rela- 
tion to affirmation. It determines that of the two forms 
given by the laws of Identity and Contradiction, and by these 
laws affirmed as those exclusively possible, ‘the one or other 
must be affirmed as necessary.’ Hamilton seems to have 
fallen into the error of supposing that the law of Excluded 
Middle is a principle of Apodicticity, and gives necessary 
results. It necessitates the affirmation of one or other of the 
opposed contradictories. It does not affirm the one or other 
to be necessary. Besides, the formula which Hamilton uses 1s 
really the formula for the joint axiom of Contradiction and 
Excluded Middle, and does not express the latter purely. 
Cf. § 79. | 

J. S. Mill! thinks that this law is one of the principles of 
all reasonings, being the generalisation of a process which is 
liable to be required in all of them. It empowers us to sub- 
stitute for the denial of two contradictory popositions the 
‘assertion of the other two. He denies in his Logic? the 
necessity and universality of the law, and says that it 18 
not even true without a large exception. A predicate must 
be either true or false, provided that the predicate be one 
which can in any intelligible sense be attributed to the sub- 
ject. Between the true and the false there is always a third 
possibility—the unmeaning. There are many valuable re- 
marks in the pages Mr. Mill has given to the discussion of 
these laws, and had he not been hampered by his empirical 
theory of the origin of all knowledge, and his consequent 
theory of the supposititious nature of demonstrative science, 
he would have approached very nearly to the doctrine laid 
down in the text. Had he only pursued the theory laid 
down in discussing propositions—that they express real rela- 
tions, he would have arrived at it. But there always seems 
to be a double view of Logic before Mr. Mill, and he shifts 
from the one to the other. On the one view Jogic is a theory 
of knowledge, on the other it is almost a theory of naming. 


ι Examination of Sir W. Hamilton’s Philos. 8rd ed. p. 473. 
2 1. 309. 


§ 79. Contradiction and Excluded Third, etc. 275 





The two views come out most clearly in the chapters on pro- 
positions. Propositions in general describe facts, but Defini- 
tions describe names. In what is said of the laws of thought 
in his Logic the former view predominates; in what is ssid in 
the Examination, &c., the latter. 

A, Bain' confuses the opposition of predicates as contra- 
dictories, with the so-called contradictory opposition of judg- 
ments, to the extent that he makes the one grow out of the 
other; while they are in no way related. He thus makes the 
law of Excluded Middle an ‘incident of partial or incomplete 
contrariety ;’ and says: ‘It is too much honoured by the 
dignity of a primary law of thought.’] 


§ 79. The axiom of Contradiction and the axiom of 
Excluded Middle may be comprehended in the formula: 
A is either B or is not B. Any predicate in question 
either belongs or does not belong to any subject; 
or—of judgments opposed as contradictories to each 
other, the one is true and the other false; or—To 
every completely distinct question understood always 
in the same sense, which has to do with the possession 
of a definite attribute by a definite subject, yes or no 
must be answered. These formulae contain the axiom 
of Contradiction, for they posit two contradictory mem- 
bers, and assert that the affirmation and denial of the 
same cannot both be true; A is either B, or is not B. 
They also contain the axiom of Excluded Third, for 
they posit only two mutually exclusive members, and 
assert, that any third besides affirmation and negation 
is inadmissible, and that both are not false, but one of 
the two is true,—a is either B or is not B; there is no 


third. The comprehension of the axioms of Contradic- 


1 Deductive Logic, p. 17.] 
T 2 














276 ὃ 79. Contradiction and Excluded Third 





tion and Excluded Third in the foregoing formula may 
be called the Principe OF CONTRADICTORY DISJUNCTION 
(principium disiunctionis contradictoriae). 


A suitable statement of the question is again the natural 
presupposition of the application of this principle. 

The transference of the denial to the predicate “A is either 
B or non-B,’—is not false, provided that, by non-B, only con- 
tradictory opposition be understood. It is a useless artifice, 
however, and easily gives rise to a false meaning in the con- 
trary opposite. 

The simplest metaphysical formula of the principle of Con- 
tradictory Disjunction is found as early as in Parmenides,! ἔστιν 
ἢ οὐκ ἔστιν. It is here used only in the sense of the axiom of 
Contradiction to reject the common truth of the assertion of 
Being and Not-Being. Being and Not-Being cannot exist 
together, the one excludes the other. 

Aristotle, on the other hand, uses the comprehensive for- 
mula mostly in the sense of the axiom of Excluded Third.’ 
ἀλλὰ μὴν οὐδὲ μεταξὺ ἀντιφάσεως ἐνδέχεται εἶναι οὐθέν, ἀλλ᾽ 
ἀνάγκη ἢ φάναι ἢ ἀποφάναι ἕν καθ᾽ ἑνὸς ὁτιοῦν. πᾶν ἢ φάναι 
ἢ ἀποφάναι ἀναγκαῖον. ἐπὶ τῆς καταφάσεως καὶ τῆς ἀποφάσεως 
ἀεὶ--- τὸ ἕτερον ἔσται ψεῦδος καὶ τὸ ἕτερον ἀληθές. 
φάναι ἢ ἀποφάναι ἡ εἰς. τὸ ἀδύνατον ἀποδειξις λαμβάνει. Ari- 
stotle tried to deduce the axiom from the definitions of truth 
and untruth, on the ground of the presupposed impossibility 
that the same could be and not be. Every judgment (because 
it is a subjective assertion about objective existence) must 
fall under one of four forms of combination: denying what 
exists, affirming what does not exist; affirming what exists, 
denying what does not exist. The first two of these are false, 
the last two are true (for in the former the thought does not 
correspond with the actual fact; in the latter it does). The 


‘ Be 
τὸ δ᾽ ἅπαν 


one assertion is true and the other false on presupposition of 


And in 


1 Fragm. vs. 72, ed. Mullach; ap. Simplic. ud Arist. Phys. fol. 31 2. 
2 Metaph. iv. 7, § 1. 3 Ib. 8, § 6. 
4 Categ. c. x. 18 B, 27. > Anal. Post. i. 11. 


Being, and also so on presupposition of Not-Being. 


in the Principle of Contradictory Disjunction. 277 





every case either the affirmation or the negation is true, and, 
therefore, since truth is what we aim at, ἢ φάναι ἢ ἀποφάναι 
ἀναγκαῖον. Both cannot be false and a Third or Middle true. 
No place is left fora Middle. For a Middle, if it be true, or 
even thinkable, and have the reference to truth and falsehood, 
which belongs essentially to every judgment, must itself be 
one of that combination of members, which it cannot be accord- 
ing to its very notion. For in the Middle neither what exists 
nor what does not exist is affirmed or denied. It is in this 
way that the incompletely expressed reasoning of Aristotle 
against the Middle or Third must be completed.! 

Leibniz? places the negative form—-“ A proposition is either 
true or false,’ by the side of the affirmative form of the pri- 
mitive, identical, rational truth—‘ Everything is what it is.’ 
He calls this axiom the principle of Contradiction, and divides 
it into the two axioms which he includes in it—‘ That a pro- 
position cannot be true and false at the same time;’ and— 
‘That there is no mean between the true and the false,’ or 
rather—It is not possible that a proposition can be neither 
true nor false. In the same way Leibniz calls, ‘ Principe de 
la Contradiction,’ the one ‘which asserts that of two con- 
tradictory propositions the one is true and the other false.’ 
Leibniz, therefore, understands by the Principle of Contradic- 
tion that axiom which includes both what is usually called the 
Axiom of Contradiction and the Axiom of Excluded Third. 

Wolff* enunciates the formulae ‘ quodlibet vel est, vel non est;’ 
“ propositionum contradictoriarum altera necessario vera, altera 
necessario falsa,’ and says, ‘patet per se, eidem subiecto A 
idem praedicatum B vel convenire, vel non convenire.’ Many, 
both of the earlier and of the later logicians, have wrongly 
believed the formula—a is either B or not B, which includes 
both the axiom of Contradiction and of Excluded Third, to 
be the proper and simple expression of the axiom of Excluded 


Third.’ 


! Metaph. iv.7, §§ 2, 6. 2 Nouv. Ess. iv. 2, § 1. 

ὁ Théod. i. ὃ 44. 4 Ontol. ὃ 52; Log. ὃ 532. 

° Cf. upon the whole question, Katzenberger, Grundfragen der 
Logik, Leipzig, 1858. 




















278 § 80. Relations between Fudgments 





§ 80. The foregoing Axioms are not to be applied to 
judgments whose PREDICATES stand to each other in the 
relation of CONTRARY opposites (like positive and nega- 
tive quantities). In this relation it is possible under 
certain presuppositions, that (a) both judgments be 
false ; and that (b) both judgments be true. 

Both may be false :— 

1. When that notion which is superordinate to the 
two predicates opposed to each other as contraries as 
their common genus-notion does not belong to the 
subject as its predicate. (Kant called this relation 
Dialectical Opposition. ) 

2. When that genus-notion belongs to the subject, 
but comprehends under it, besides the two predicates 
opposed as contraries to each other, other species-notions. 
In this last case the axiom of the Third lying as a mean 
between two contrary opposites finds application (prin- 
cipium tertii intervenientis inter duo contraria ). 

Both may be true :— 

When the subject denotes an object, which is neither 
absolutely simple nor yet a mere aggregate, but is a 
synthetic unity of manifold determinations. When 


some of these determinations or attributes stand in the 


relation ‘of contrary opposites to each other, the axiom 
of Coincidence may be applied to them (principium 
coincidentiae oppositorum). All development by strife 
and union of opposites rests on this principle. 


Judgments, whose predicates are opposed to each other ὁ 
contraries (§ 53)—e.g. Caius is happy, Caius is sad—are to be 
strictly distinguished from judgments which are contrarily 
opposed to euch other as judgments ($ 72)—e.g. all men are | 


whose Predicates are opposed as Contraries, ete. 279 





learned, no men are learned. The former may not only both be 
false, but in a certain sense may both be true. For example, 
both joy and sorrow are contained in the feeling of yearning. 
The latter cannot both be true, but both may be false (ᾧ 97). 
From both of these relations we must distinguish the relation 
of Contradictory Opposition, whose members cannot both be 
true nor both false (§ 79); for example—Caius is happy, Caius 
is not happy ; all men are learned, some men are not learned. 

Plato teaches that one and the same thing may unite in itself 
qualities which are different and even opposed to each other, 
although the quality itself is never identical with its opposite.’ 

In a similar way, Aristotle explains that the object may 
change because it may take properties which are opposed to 
each other, but that the property itself always remains the 
same in its notion.? Since Aristotle says distinctly, that only 
contradictory opposites exclude every mean, he makes a mean 
possible in contrary opposites? (ἐπὶ yap μόνων τούτων ἀναγκαῖον 
ἀεὶ TO μὲν ἀληθές, τὸ δὲ ψεῦδος εἶναι). 

Later logicians have seldom thought the relations οὗ judg- 
ments with predicates opposed as contraries worthy of more 
particular attention. 

Augustine says, in his short doctrinal epistle to Laurentius :* 
—QOmnis natura etiamsi vitiosa est, in quantum natura est, 
bona est, in quantum vitiosa est, mala est. Quapropter in his 
contrariis, quae mala et bona vocantur, illa dialecticorum regula 
deficit qua dicunt nulli rei duo simul inesse contraria. Nullus 
enim aér simul est et tenebrosus et lucidus, nullus cibus aut 
potus simul dulcis et amarus, nullum corpus simul ubi album 
ibi et nigrum . . . . sed mala omnino sine bonis et nisi in bonis 
esse non possunt, quamvis bona sine malis possint. But he 
does not strictly distinguish Contrary from Contradictory 
Opposition. 

Nicolaus Cusanus, and after him Giordano Bruno, were the 


1 Phaedon. p. 1038; cf. Soph. p. 257 Β, where the ἐναντίον is dis- 
tinguished from the ἕτερον. 

2 Metaph. iv. 5, ὃ 40. 8 Ibid. iv. 7, ὃ 1; cf. Categ. x. 138, 2. 

4 De Fide Spe et Caritate, c. v. 


























280 § 80. Relations between Fudgments, etc. 





first to enunciate expressly the principium coincidentiae oppo- 
sitorum. 

Kant rigorously distinguishes the opposition of contrary 
predicates from contradiction. Judgments of the first kind can 
both be false. For example, it is equally incorrect to attribute 
the predicates of limited and unlimited to what has no existence 
in space; beginning in time, and beginningless, endless dura- 
tion in time, to the timeless. The opposition here is only 
‘dialectic,’ or apparent.’ 

Hegel and Herbart, as has been shown above, make no dis- 

tinction between the oppositions, but do this in opposite ways. 
The insight that the form of all development in the life of 
nature and mind (Geist) is-the development of (contrary) op- 
posites out of the indifferent or the germ, and their union in a 
higher unity, is to be recognized as an abiding result of the 
speculation of Schelling and Hegel. 
. In the same sense, 1. H. Fichte? while he condemns the 
exchange,’ says quite correctly,‘ ‘ est enim ubertas rei quaedam, 
si opposita ad se referre et in se copulare possit;’ and T'rende- 
lenburg, who shows the dialectic method of Hegel to be an 
exchange of logical negation for real opposition,’ recognises 
that® ‘solet quidem natura, quo maiora gignit, eo potentius, 
quae contraria sunt, complecti.”’ 

If contrary opposites-could not unite in any way there could 
be no multiplicity or development. Everything would be as 
Parmenides believes, ‘ The One alone truly exists ;’ or as Her- 
bart, in a milder way, expresses it, ‘ Each one of the many is 


1 Krit. der.r. Vern. 2nd ed. p. 531 ff. 

2 De Frinc. Contrad. 1840; cf. Ontol. p. 159, 1836, where he in- 
correctly makes ‘ Unterschied’ (Difference) and ‘Gegensatz’ (Oppo- 
site) equivalent to ‘ Contrary ’ and ‘ Contradictory,’ p. 165 ff. 

8 P. 25. ı P. 28. 

5 Log. Unters. 2nd ed. i. 43; 3rd ed. i. 43. 

6 Elem. Log. Arist. ad ὃ 9, p. 65, 3rd ed.; cf. Log. Unt. 2nd ed. 
ii. 234; 3rd ed. ii. 257. 

7 Cf. also the work mentioned above (§ 69), Gustav Knauer, Conträr 
und Contradictorisch, Halle, 1868. 


§ 81. Zhe Axiom of Sufficient Reason. 281 





simple and unchangeable, unalterable, persisting in its simple 
quality.’—If contrary opposites were not relatively indepen- 
dent (or if contradictory opposites even could be united), there 
could be no unity nor persistence. Everything would be as 
Heraclitus, and in a more logically definite way Hegel, be- 
lieves.—‘ Everything fleets. Everything is like and also not 
like itself. Nothing is definable by a permanent notion.’ In 
reality both unity and plurality, persistence and change, exist 
together. And the one not exclusive of the other, as Plato 
represents by Ideas and Sensible Things, or as Kant almost 
similarly represents by his ‘Ding an Sich’ and phenomena. 
They exist, as was partly taught in antiquity by Aristotle and 
the Stores, and in our time has been taught by Schleiermacher 
in a purer and deeper way, in, with, and through each other; so 
that the uniting essential form and force dwells in the multi- 
plicity of phenomena, and inviolable law rules the change of 
actions. 


$ 81. THe Axiom OF THE (determining or sufficient) 
Reason subjects the deduction of different cognitions 
from one another to the following rule:—A judgment 
can be derived from another judgment (materially dif- 
ferent from it), and finds in it its sufficient reason, only 
when the (logical) connection of thoughts corresponds 
to a (real) causal connection. The perfection of the 
knowledge lies in this, that the ground of knowledge is 
coincident with the real ground. The knowledge of a 
real interdependence of things conformable to law is 
reached, as (δὲ 42-42; 46; 57; 73) the knowledge of 
the inner nature of things in general, and more espe- 
cially of the individual existence, of the essence, and of 
the fundamental relations are reached. The external 


invariable connection among sense-phenomena is with 
logical correctness explained by an inner conforma- 




















282 § 81. The Axiom of Sufficient Reason. 





bility to law, according to the analogy of the causal 
connection perceived in ourselves, between volition and 
its actual accomplishment (whose existence we learn 
for the most part by striving against what resists us). 


The real conformability to law reveals itself in the simple 
regularity of external and especially inorganic nature in a way 
more evident and more fitted to arrest the attention, than in 
the manifoldly complicated psychic processes. Yet these are 
the only cases, in which the peculiar character of that con- 
formability to law as the realisation of the internal powers, 
is immediately accessible to observation. So long as the man 
has no presentiment of an internal conformability to law, what 
happens externally is also referred to the lawless caprice of 
imaginary agents. 

A genetic treatment finds a thoroughgoing causal conform- 
ability to law in the (objectively real) relations with which 
mathematics has to do. The objective interdependence between 
quantities and between forms exists in and for itself, when not 
recognised by the subject. On this objective interdependence 
the physical processes rest, which exist independently of the 
knowing subject, and condition the possibility of existence of 
knowing subjects. On the objective nature of quantity and of 
space that conformability to law is established, which Kant re- 
ferred falsely to a subjective origin. 

The logical form of axiom given above only asserts that the 
combination of judgments, by which a new one is derived from 
given ones, must rest on an objective causal nexus. Whether 
and in what sense everything objective stands in causal relations 
is to be decided elsewhere (in Metaphysics and Psychology). 

Plato and Aristotle make the thoroughgoing agreement (ὁμο- 
λογία, ξυνάδειν, ξυμφωνεῖν) of cognitions with each other and 
with their grounds, an essential condition of their truth. 

Plato teaches :'! πᾶν τὸ γυγνόμενον ὑπ᾽ αἰτίου τινὸς ἐξ ἀνάγκης 
γέγνεσθαι" παντὶ γὰρ ἀδύνατον χωρὶς αἰτίου γένεσιν σχεῖν. 

1 Tim. p. 28 A. 
2 Cf. Phaedon, pp. 100 a, 101 D; De Rep. vi. 511. 


§ 81. The Axtom of Sufficient Reason. 283 





-.-..... 


Aristotle places the essence of science in the adequate know- 
ledge of causes. The syllogism warrants this knowledge, since 
the middle notion corresponds to the real ground.' Aristotle 
distinguishes, in his Metaphysics, four principles or causes 
(ἀρχαί or αὐτίαι) : Matter, Form, Cause, and End ;? but with 
reference to our knowledge he distinguishes the grounds of 
Being, Becoming, and Knowing.* πασῶν μὲν οὖν κοινὸν τῶν 
ἀρχῶν τὸ πρῶτον εἶναι ὅθεν ἢ ἔστιν ἢ γίγνεται ἢ γυγνώσκεται" 
τούτων δὲ αἱ μὲν ἐνυπάρχουσαί εἰσιν, αἱ δὲ ἐκτός. 

The axiom, ‘ Nihil fit sine causa’ was in use among the 
ancients as an axiom of Physics. Cicero quotes it against 
Epieurus,* ‘ Nihil turpius physico, quam fieri sine causa quid 
quam dicere.’ 

Suarez ‘Omnia alia, praeter ipsum (Deum), causam 
habent.’ 

Jacob Thomasius® distinguishes ‘ Omne ens, quod fieri 
dicitur, habet causam efficientem ;’—* Christianis omnino statu- 
endum est, canoni praesenti locum esse quoque universaliter 
in causa finali. 

Leibniz was the first who expressly placed the axiom of 
Determining (or as he afterwards called it) of Sufficient Reason, 
side by side with the axiom of Contradiction, as a principle 
of inference. He says,”—* It is necessary to remember that 
there are two great principles of our reasoning; the one is 
the principle of Contradiction ; the other, that of “la raison 
déterminante,” which is, that nothing can be concluded, with- 
out it has a determining cause, or at least reason.’* ‘Our 
intellectual inferences rest on two great principles: the prin- 
ciple of Contradiction, and the principle of Sufficient Reason, 
in virtue of which we know that no fact can be found real, no 
proposition true, without a sufficient reason, why it is in this 
way rather than in another.’ In his Second Letter to Clarke 


Arist. Anal. pt. I. 32; Eth. Nicom. i. 8; Anal. Post. i. 2; ii. 2. 
Metaph. i. 3, § 1 and elsewhere. 3 Ibid. v. 1, § 9. 
De Fin. i. 6, 19, and elsewhere. 5 Metaph. i. 259. 
Dilucid. Stahlianae, ὃ 127. 7 Théod. i. § 44. 

' Monadologie (Princip. Phil.), ὃ 80 sqq. 























288 § 81. The Axiom of Sufficient Reason. 





Leibniz also calls this principle, ‘ Principium Convenientiae.’ 
At the end of the fifth letter to Clarke he makes the same 
threefold distinction as Aristotle :! ‘ This principle is that of a 
sufficient reason, why a thing exists, an event happens, a truth 
has place.’ The first and second refererices belong to Meta- 
physics, the third to Logic. 

Wolff? and Baumgarten? seek to deduce the axiom of the 
Reason from the axiom of Contradiction, because they believe 
that the latter is the only absolutely ἃ priori principle (which 
is to be combined with Experience however). If the ground 
of a thing lies in nothing, then nothing is the ground or reason 
itself. But this contains the contradiction, that nothing, as an 
actual principle, is also something. The mistake in this de- 
duction (the misinterpretation of the expression ‘ nothing is 
the ground,’ because of a false realisation of ‘ nothing’) was 
pointed out by contemporaries. Wolff,‘ following Leibniz, 
explains the axiom of Contradiction to be the ground of 
necessary, and the axiom of Sufficient Reason, the source of 
accidental truth. 

Kant® thus enunciates the “Law of Causality:’ < All 
changes happen according to the law of the connection of 
cause and effect.’ He considers this to be a synthetic axiom 
a priori, and a ground of possible experience, or of the ob- 
jective knowledge of phenomena, in view of their relation in the 
course of succession in time. He does not allow that it is 
applicable to ‘ Things-in-themselves.” In Logic, Kant ex- 
plains the ‘ axiom of sufficient reason’ to be the principle of 
assertory judgments.’ He gives it® the form—‘ Every pro- 
position must have a reason.’ He makes this logical principle 
not co-ordinate with, but subordinate to the axiom of Contra- 
diction. On the other hand, the transcendental or material 


I Metaph. v. 1, ὃ 9. ? Ontol. § 70 sqq.; cf. Metaph. § 30 ff. 
Metaph. § 20. * Annot. ad Met. p. 9 ff. 
5 Prine. Phil. ὃ 30 sqq.; Epist. ii. ad Clare. 
6 Krit. der r. Vernunft, p. 232 ff. 7 Log. ed. by Jäsche, p. 73. 
8 In the treatise Ueber eine Entdeckung, &c. Works, ed. by Har- 
tenstein, vi. 1 ff. 


§ 81. The Axiom of Sufficient Reason. 285 





principle, ‘every thing must have a cause,’ is in no way 
derivable from the axiom of Contradiction. 

On the basis of the Kantian theory Arthur Schopenhauer! 
asserts that the principium rationis sufficientis essendi, fiendi, 
agendi, and cognoscendi, are the four fundamental forms of 


synthesis ἃ priori. 

Hegel (following Fichte and the Neoplatonists) resolves the 
law of the Reason,—‘ Every thing has a sufficient Reason,’ 
into the law of the combination of opposites,—‘ The reason is 
the unity of Identity and Difference.’? | 

Herbart* seeks to explain the real (causal) nexus by means of 
his theory of the self-conservation of simple essences, in oppo- 
sition to their disturbance by conflict with others; and to solve 
the question of how antecedent and consequent may be con- 
nected, by his so-called ‘method of references,’ i.e. by the 
hypothetical completions of what is given, which prove them- 
selves necessary by the fact that the law of Contradiction re- 
mains unviolated only when they are accepted. 

According to Schleiermacher,' the (causal) necessity rests on 
the inter-dependence of the system of the co-existence of Being, 
or on ‘ Actions,’ just as freedom does upon its existence in and 
for itself—as ‘power.’ The true view is contained in the 
definitions of Hegel, Herbart, and Schleiermacher. It is that 
the whole cause is made up of the inner ground and the outward 
conditions.» A more exhaustive representation and proof of 
this doctrine would lead us away from the province of Logic 
into that of Metaphysics. ei 

Delboeuf, agreeing with the views laid down in this para- 
graph, enunciates as the principle which makes legitimate all our 
inferences (raisonnements) the axiom, ‘ The logical concatena- 
tion of the ideas corresponds to the real concatenation of things.’° 

[J. S. Mill’ says that the most valuable truths relating to 
phenomena are those which relate to the order of their succes- 


I Ueber die vierfache Wurzel des Satzes vom zureichenden Grunde. 
2 Logik, i. 2, p. 72 ff.; Encycl. ὃ 121. 

3 Allg. Metaph. ii. 58 ff. 4 Dial. p. 150 and elsewhere. 

5 Cf. ὃ 69. 6 Cf. § 75. [7 Logic, i. 800. 

















286 =§ 81. The Axiom of Sufficient Reason. 





sion. In order to know such truths we must endeavour to 
find some law of succession-which has the same attributes, and 
is therefore fit to be made the foundation of processes for dis- 
covering, and of a test for verifying all other uniformities of 
succession. This fundamental law is the ‘ Law of Causation’ 
—‘ every fact, which has a beginning, has a cause.’ The notions 
which are combined in this formula, along with the law it 
expresses, are gained by experience. Invariability of succes- 
sion is found by observation to obtain between every fact in 
nature and some other fact which has preceded it. The suc- 
cession is not usually between one antecedent and its conse- 
quent. The processes of nature are complicated. ‘ The cause 
is the sum total of the conditions, positive and negative taken 
together ; the whole of the contingencies of every description, 
which being realised, the consequent invariably follows.’ On 
this law every inductive truth rests, and to it every inductive 
process must be referred. 

A.’ Bain" believes that there must be some guarantee for 
every real inference, and that the sole guarantee is the Uni- 
formity of Nature. Now uniformities of Nature are either of 
co-existence or succession. The evidence for uniformities of co- 
existence is special observation of each separate uniformity. 
In uniformities of succession the labour has been shortened by 
the discovery of a law of uniformity—the law of Causation. It 
may be expressed thus :—-‘ Every event is uniformly preceded 
by some other event.’ The most important form of the law of 
Causation is what Mr. Bain calls the ‘law of the conserva- 
tion of force which encompasses and pervades all the natural 
sciences, each one of which is but a partial development of it.’ 

Sir W. Hamilton, in his lectures,? enounces a law of Reason 
and Consequent, which he says is the foundation of the Hypo- 
thetical Syllogism. He expresses it, ‘ Infer nothing without a 
ground or reason.’ In the Appendix to his Lectures, however, 
and in his Discussions, he refuses to admit this law, saying that, 
(1) inasmuch as it is not material it is a derivation of the three 
formal laws of Identity, Contradiction, and Excluded Middle : 


1 Deductive Logic, pp. 18-20. εὖ De 


§ 82. Forms of Immediate Inference in General. 287 





and (2) inasmuch as it is material, it coincides with the prin- 


ciple of Causality and 15 extralogical. | Veit as Brite 
The Leibnizian principium identitatis indiscernibilium' can 


only be expounded in Metaphysics, not in Logic. 


§ 82. The Forms of Immediate Inference are : partly 
—The derivation of a judgment from a notion, i.e. the 
analytical formation of notions ; and partly— The deriva- 
tion of a judgment from a judgment. | 

There are seven kinds of this latter derivation, viz. : 
(1) Conversion; (2) Contraposition; (3) Change of 
Relation; (4) Subalternation; (5) Aequipollence ; (6) 
Opposition ; (7) Modal Consequence. 

Conversion has to do with the position of the elements 
of the judgment within its Relation, and often indirectly 
with the Quantity. 

Contraposition has likewise to do with the position of 
the elements of the judgment in its Relation with the 
Quality, and often indirectly with the Quantity. 

Change of Relation has to do with the Relation itself. 

Aequipollence refers to Quality ; Opposition to Quality 
and indirectly to Quantity. 

Modal Consequence has to do with the Modality of 


the judgment. es 
All these deductions rest on the axioms of Identity 


and Contradictory Disjunction. 


Aristotle discusses Conversion (ἀντιστρέφειν, ἀντιστροφή); 
which he places at the service of Syllogistic,’ the relation of 
Opposition (dvrietcOa),3 and Modal Consequence." He 


1 Princ. de la Nature et de la Grace, § 9; Epist. iv. ad Clarc., 
non dantur duo individua plane indiscernibilia. 

* Anal. Pri. i. 2; 13; 17. 3 De Interp. c. vii. ff. 

4 Ibid. ce. xiii. 








quite 


HW 
N 
; 
i 
4 
Bi 
ee u 
1 
| 
it 
4 
u 
ἽΝ 'F 
ht} 
| 
ihe 
) N 
ΠΗ 
MIR 
Nii) nee 
fl | 
{ΠῚ 
N 
| Ἵ 
ἡ}. 
AW bi 
hl 
IF 
ἡ} ἢ 
Hie 
Nias 
Ἷ ἢ 
*. 





es a nn 


288 § 82. Forms of Immediate Inference in General 





recognises Subalternation only as an element of the syllogistic 
formation of inferences, not as an independent form. He says! 
the proposition not-man is not just, is equivalent to the propo- 
sition no not-man is just. This contains qualitative Aequi- 
pollence. 

The name Aequipollence (referred to equivalent judgments 
in a wider sense) was first introduced by Galen, the author of a 
work περὶ τῶν ἰσοδυναμουσῶν προτάσεων. Galen distinguished 
between ἀντιστρέφειν, by which he understood Contraposition, 
and ἀναστρέφειν, by which he meant Conversion. He applied 
both terms to categorical and also to hypothetical judgments, 

Appuleius seems to have been the first to use the Latin term 

aequipollens in his definition: “ Aequipollentes autem dicuntur 
(propositiones), quae alia enunciatione tantundem possunt et 
simul verae fiunt aut simul falsae, altera ob alteram scilicet,’ 

Boéthius calls equivalent judgments indicia convenientia or 
consentientia. He uses the phrase conversa per contra posi- 
tionem for Contraposition, and calls Conversion in the strict 
sense Conversio Simplex. Simple Conversion is accomplished 
either principaliter, i.e. without change of quantity, or per 
accidens, i.e. with change of quantity. In other respects, 
the terminology employed by Boéthius is the same as ‚that of 
the Scholastic and of modern formal logic.? 

Wolff does not call immediate inferences ratiocinatio (because 
he means by ratiocinatio the deduction of a third judgment 
from two given ones only). He calls them consequentias 
immediatas.* He explains them to be abbreviated hypothetical 
syllogisms ;‘ and accordingly discusses them after Syllogism. 

Kant,’ and most modern logicians along with him, have 
reversed the order. Kant founds the division of immediate 
inference on his table of Categories. Subalternation, accord- 


ing to his view, rests on Quantity ; Opposition on Quality 
( . . . . 

(Aequipollence is only a change of the expression in words, 
and not a form of judgment); Conversion on Relation ; and 


I De Interp. c. x. 20 a, 39. 
5 Cf. Prantl, Gesch. der Logik, i. 568 f.; 583, 692 fF 
3 Log. $ 459. 4 Ibid. § 460. 5 Log. § 41 ff. 


ἢ 83. Analytical Formation of the Fudgment, etc. 289 











Modality. The later logicians have mostly 


f the Kantian division, but have sought 
many insufficiencies 


Contraposition on 
kept by the principle o 


to remedy, with greater or less success, 


1 ie 1 1 t. 
which lie in the Kantıan statemen 

The Analytic Construction of Judgments should not be 
reckoned among immediate inferences (and was not in the first 


edition of this Logic); but belongs to this species of inference. 


§ 83. The Analytic F ormation of Judgments rests on 
the axiom ($ 76) that every attribute may be posited 
as a predicate. The distinction between Synthetic and 
Analytic Judging belongs to the genesis of judgments. 


dgment is so far synthetic, that it, according to 


Every ju 8 
ae of the real validity 


the definition, is the consciousness 
of a combination (synthesis) of conceptions. But the 
synthesis of the members of the judgment may originate 
in different ways, either immediately by the combination 
of the conceptions presented, or mediately by the ana- 
of a whole conception earlier formed, in which 
mbers of the judgment are already contained 
In the former case the con- 
in the latter 


lysis 
the me 
in an undeveloped form. 


struction of the judgment is synthetic, | 
it is analytic. The judgment derived analytically from 


the notion of the subject, is valid only on the pre- 
supposition of this subject-notion The validity of the 
subject-notion can never be inferred from it. 


ject is the conception otherwise 


In every judgment the sub cept 
definite, but in reference to the predicate still indefinite. In 
accused man is guilty, This accused man 


is not guilty—the subject is the conception of the accused al 
son, so far as he is a distinct person who stands under -" 
accusation; while the connection of the conception of sas 
with the conception of the subject still remains an open ques- 


the propositions— This 


U 











290 § 83. The Analytical Formation 








tion, i.e. an indefiniteness, which may be made definite, and is 
made definite by the acceptation or rejection of the predicate 
notion. In the judgment—The earth is a planet—the case is 
the same. The subject, the earth is on other sides definite, 
perhaps as γῆ εὐρύστερνος, πάντων ἕδος ἀσφαλὲς αἰεί; but in 
reference to what the predicate asserts it is still indefinite. 
The judgments—Iron is metal, every body is extended, the 
Quadrate is a parallelogram—have sense and meaning only in so 
far as he who judges has left a place in his notion of the subject 
for the determination given in the predicate, but does not yet 
know this determination. He conceives iron perhaps by imme- 
diate sense intuition. He understands by body the perceivable 
thing, about which it is not quite determined whether it is 
always extended or not. He conceives the square as an equi- 
lateral rectangular four-sided figure, without being conscious 
that the opposite sides are parallel. The subject of a definition 
denotes the thing only as that to which the name belongs. The 
predicate brings the closer determination, which was left inde- 
finite in the conception of the subject. Thus allthese judgments, 
according to their character, are synthetic. It is only the mode 
of making the synthesis of the parts of the judgment that is 
different. Recourse to the definition of the subject-notion, in 
the analytical construction of judgments, means to call into 
one’s consciousness the moments which would not have been 
thought along with the name alone. In the synthetic construc- 
tion of notions the synthesis may be accomplished either by 
perception or by an inference. The inference rests either on 
circumstances known otherwise (as in the proof by witnesses of 
the guilt of the person accused), or upon attributes thought 
expressly in the notion of the subject itself. The necessary 
connection of the attributes thought in the predicate is recog- 
nised from these because of a causal relation of dependence 
(e.g. from the equality of sides, the equality of angles in a 
triangle). The last named way often exists where Kant 
speaks of a ‘ synthesis ἃ priori.’ 
Thomas of Aquino! and others explain identical propositions 


I Summa Theol. i. 2. 1: 





of the Fudgment, etc. 291 





to be absolutely certain, on the basis of the Aristotelian axıom 
; iction.! 
a Des, on “ frivolous propositions,’ μείνουν en 
only repeats the notion of the subject or single pr we 6 — 
Hume’s distinetion? between ‘ relations of ideas and ‘ matter: 
of fact, paved the way for the Kantian es ER 
" Leibniz‘ held that all the primitive intellectual truths 
identicz ositions. a“ 
ee of the Axiom—propositio en 
monstrabilis — embraced, besides the identical ee Ἢ 
those also which were derived from identical oe y 
analysis and combination. The difficulty, which Kant Ἕ οὐ 
wards indicated by the distinction between analy Ee anc = 
thetic judgments, is concealed behind the rn > 
expression, in those places in his Logic’ where v olf = Sr 
the relation in question. He says, ‘ propositio ila bs . 
monstrabilis dicitur, cuius subjecto convenire vel non in e 
praedicatum terminis intellectis patet.’ He tries to make 
phrase ‘terminis intellectis patet’ evident by er 4 
explains it partly in this way, that we are to under re 7 
the warrant that those predicative u ey = 
belong to the notion of the subject, as it 1s exhi ag ὶ = 
definition, are yet inseparably connected with it > © eg "πῇ 
praedicato respondent, ab iis, quae ad subiecti mie ee 
mus sive quae ad definitionem eius pertinent, separarl nol J = 
animadvertimus.’ Wolff does not state the reason : 2 2 
inseparability. Hence he is not conscious of the μύρα: en 
if the predicate be found by merely going back to t u ( με τε 
of the subject, and to the definitions of single notions whic = 
found in the definition of the subject, the rer u a 
merely an analytical judgment, which has indeed apoc sie 
tainty, but does not extend our knowledge. (His examples ¢ 
I Cf. Arist. De Interp. c. xi. 2 Essay iv. 8; cf. 3, 7. 
3 Enquiry iv.; cf. Locke, Ess. iv. 4, 6. 
Nouv. Ess. iv. 2; Monadol. § 35. 
Ibid. §§ 268, 270, 273; cf. 264. 
Ibid. § 262. 


5 Logik, § 267. 
7 Ibid. § 261 ff. 





292 § 83. The Analytical Formation 





specimens: The whole is greater than a part; Radii of the 
same circle are equal to each other, &c.; and the case appears 
to be universally the same, according to the Leibnizo- Wolffian 
axiom that all primitive intellectual truths are identical propo- 
sitions.) Nor does he see that if to go back to the definition of 
the subject is not sufficient, and if the predicate constitutes an 
essentially new determination, which is not contained in the 
content of the subject-notion given in the definition, as far as 
analysis leads us, our knowledge may be enlarged, but we 
want a ground of certainty for this enlargement. This is the 
point where Kant, who got his impulse from other sides also 
(viz. from the investigations of Locke and Hume), finds the 
first motive to an advance beyond the stand-point of Leibniz 
and Wolff. 

Kant! rightly distinguishes the analytical and synthetieal 
formation of judgments, however wrongly he may transfer the 
distinction to the judgments themselves. 

He calls Analytical Judgments those in which the connection 
of the predicate with the subject rests on the relation of identity 
(e.g. a=a, or, All bodies are extended ; which depend on the 
definitions : equality is identity of size; body is extended sub- 
stance). These do not assert in the predicate anything beyond 
what is already thought in the notion of the subject, although 
not with the same clearness or strength of consciousness. They 
are merely explanatory judgments. 

He calls Synthetic Judgments those in which the connection 
of the predicate with the subject does not rest upon the relation 
of Identity (e.g. the straight line is the shortest between two 
points; or, every body is heavy. These examples proceed on 
the presupposition that shortness does not enter into the defini- 
tion of the straight line, nor weight into the definition of body. 
If the notion of the subject were already so defined and limited 
the judgments would be analytic). In these judgments there 
may be a necessity, belonging to the subject, to think the pre- 
dicate along with it; but the predicate is not actually, nor ina 

! Krit.der r.Vern., Einl. iv.; Proleg. zu einer jeden künftigen Metaph. 
§ 2; Log. § 36. 


of the Fudgment, etc. 293 





covert way, thought in the subject. Synthetical judgments 
are ampliative judgments. | 

Hegel, by his dialectic method, seeks to do away with the 
distinction of analytic and synthetic judgments by means of the 
notion of development. He says,' “ Dialectic progression is the 
established judgment of the Idea ;—this progression is both ana- 
lytic, because by the “ immanent” Dialectic that only is posited 
which is contained in the immediate notion, and synthetic, 
because the distinction has not yet been posited in this notion.’ 

This method is itself untenable. A smaller content has no 
power in any way to make itself increase to a larger content. 
The genuinely scientific formation of notions demands that the 
subject should be regarded as the germ out of which the dif- 
ferent predicates grow. For example, the notions of circle, of 
gravitation, &c., may be looked upon as the germ, the capacity, 
the dynamis, in which lie unfolded the rich manifoldness of 
geometrical propositions or judgments in the doctrine of the 
circle, in astronomical knowledge, &c. But the germ, the 
dynamis, that which Hegel calls the In-itself-ness ( Ansichsein), 
is only the inner ground of the development. The external 
conditions must be added if the development is to be more 
than a mere analysis, and is to lead not only to the bringing 
into stronger consciousness the content already present, but to 
an enlargement of content. In the above examples, straight 
lines, such as sines, tangents, secants, &c., must come into 
relation with the circle; the masses and distances of the 
heavenly bodies into relation with the principle of gravitation. 
In short, elements must enter which, in relation to this 
subject at least, are separately acquired, and are not to 
be obtained or (to use Kant’s word) “ picked out’ (heraus- 
klauben) of it. Without this external element the methodic 
procedure would be analytic (the mere assertion of what 
already lies in the subject), not synthetic (no enriching the 
content, no advance to new predicates). With this external 
element it is synthetic, but no longer analytic. The point of 
view of development in the construction of the judgment, 


I Encyel. ὃ 239. 





294 § 84. Conversion in General. 





and in all provinces of philosophical thinking, is essential; but 
the dialectic method has not been able to do away with the 
necessity of the Kantian distinction. 

Schleiermacher !' explains the distinction between the analy- 
tic and synthetic judgments to be a fleeting and relative 
one. The same judgment can be analytic and synthetic, 
according as what is said in the predicate has or has not yet 
been included in the notion of the subject. But the distinc- 
tion holds in reference to any single subject standing by itself. 
The incomplete judgment (which contains only the subject 
and predicate) is more analytic, the complete (which contains 
the object also) is more synthetic, the absolute judgment 
(whose predicate is the world) is again analytic. It must be 
urged, however, against Schleiermacher that the distinction of 
the analytic and synthetic character of the judgment is not 
connected with its completeness or incompleteness. 

Delbveuf says? the advance of science consists in this, that 
synthetical judgments change to analytic, i.e. predicates sub- 
joined empirically into those which exhibit necessity. This 
thought, in itself quite correct, is not so in relation to Kant’s 
distinction. The meaning which Delboeuf gives to the ex- 
pression is essentially different from the Kantian terminology, 
according to which an apodictic connection, which rests on a 
known causal relation, is synthetic. 

[ J. S. Mill's distinction of propositions into verbal and real; 
those which ‘assert of a thing under a particular name, only 
what is asserted in the fact of calling it by that name,’ and 
those which predicate ‘some attribute not connoted by that 
name; ’ corresponds very nearly to Kant’s distinction between 
analytic and synthetic propositions.* ] 


$ 84. Conversion is that change of form, by means 
of which the parts of a judgment change their place in 
reference to its relation. 
1 Dial. §§ 155, 308-9; Beilage, E. \xxviii. 5. 


2 Proleg. philos. de la Geom. p. 46 ff. and Log. p. 103. 
3 Cf. Logic, i. 119 ff. 


| 
| : 
| 


Its Inner Authorisation. 295 





In the categorical judgment the subject becomes pre- 
dicate and the predicate subject ; and in the hypothetical 


judgment, the conditioning proposition becomes the con- 


ditioned, and the conditioned the conditioning. 

The conversion of the categorical judgment is in- 
ternally correct, only when the notion of the predicate 
can itself become substantive, 1.6. when the sum 
total of the objects, to which what is designated by the 
predicate-notion belongs, are all of the same kind, or 
are a class or genus (in the sense of $ 58). For in this 
case, these objects only can be comprehended under a 
substantive notion, which can become a subject-notion 
(according to $ 68), while the earlier subject-notion, 
from its connection with the auxiliary notion of exist- 
ence, may refer to a relation of inherence, and so take 
the predicative form (cf. $ 68). 

The internal correctness of the hypothetical judgment, 
generally, lies under no limitation, because it denotes 
only a causal nexus, whether in the direction of from 
cause to effect, from effect to cause, or from effect to 
effect. When relations of time come into consideration, 
the first presupposition is the most natural, and there- 
fore the consequent, because the antecedent in Conver- 
sion is frequently to be expressed in the form of a final 
judgment (If it be—then must, &c.). 


The question of the internal correctness of Conversion was 
not discussed by Aristotle. The Aristotelian principle, that 
the elements of thought generally correspond to actual exist- 
ence, and that the subject and predicate especially, which find 
expression in the ὄνομα and ῥῆμα, must correspond to the 
thing, and to the action or quality, forms the basis for such 
a discussion; but Aristotle did not apply it to Conversion. 





296 § 84. Conversion in General, ete. 





The possibility of making the predicate substantive ' is a tacit 
presupposition, but is not further discussed. The post-Aris- 
totelian and the modern formal Logic have still more neglected 
metaphysical relations referred to. Schleiermacher? has hinted 
at it, and T'rendelenburg* has remarked that in Conversion 
‘The Accident is raised to be Substance,’ (or rather) that the 
substance in which it inheres becomes the object thought 
of instead of the attribute inhering; but it does not follow 
from this, that Conversion, if we except the case of the univer- 
sal negative judgment, is ‘ a mere artifice of formal Logic,’ and 
can lead to no sure result. Logic, as a doctrine of knowledge, 
can and ought to investigate what and how much follows by 
conversion‘ from a single given judgment, presupposed to be 


δ Anal. Prior. i. 2. 2 Dial. § 325. 

3 Log. Unters. 2nd ed. ii. 303; 3rd ed. ii. 336. 

4 The stand-point of logical treatment is completely mistaken, and 
numerous mistakes are inévitable in particular cases, when this investi- 
gation is supposed to be undertaken in order to ‘teach and make 
possible an arbitrary thinking, according to artificial rules and for- 
mulae,’ or to ‘reduce thinking to a mechanical schema, in order to 
proceed arbitrarily according to this schema, so that we require to 
think according to the schema only, and not according to the notions.’ * 
One might as well reproach the mathematico-mechanical procedure with 
being one-sided and arbitrary, if it investigates what follows simply 
from certain simple presuppositions, and looks at these apart from 
other data, from which they can never be actually separated. If, for 
example, the path and position of a projectile be computed solely on 
the ground of gravitation and inertia, without taking into consideration 
the influence of the resistance of the air, the concrete intuition will 
apparently determine the result more strictly and more accurately than 
the computation. But if mathematical mechanics did not use this 
abstract procedure the laws of motion could not be known, and 
the science would be ruined. It is true that there is commonly 
more than merely one judgment given to us, and that we ought to 
know more about the relation of the spheres of its subject and pre- 
dicate from other sides than that only which the judgment, con- 
sidered purely in itself, shows. Ifthe given judgment be: All men are 





* J. Hoppe, Die gesammte Logik, Paderborn, 1868. 


297 





— 


internally correct. It must also show on what this internal 
correctness depends. 

The conversion of the disjunctive judgment, whether cate- 
gorical or hypothetical, does not require special rules any more 
than the conversion of the copulative or any other co-ordinated 
judgment. Its rules come directly from the laws of the Con- 
version of simple judgments. The hypothetical judgment is also 
the type for the cognate kinds of judgments. 


$ 85. By Conversion there follows— 


I. From the Universal affirmative categorical judg- 
ment (ofthe form a): Every Sis P, 

The particular affirmative judgment (of the 
form i): At least one or some P are S (at 
least a part of the sphere of P is δ). 

From the Universal affirmative hypothetical 
judgment: whenever A is, B is, 

The particular affirmative: At least once or 
sometimes, when B is, A is (at least in part 
of the cases, where B is, A is). 

The prvof lies in the comparison of the spheres. 


mortal, or: All men are sensible-intellectual dwellers on earth, we 
know in other ways that there are also other mortal beings, but that 
there are no other sensible-intellectual inhabitants of earth. He who 
keeps to the example, and adds the other knowledge got in another 
way, can, without the trouble of abstraction, attain a completer result 
than the judgment which results according to the rules of Logic from 
a single given judgment, and so can very easily, on the ground of 
supposed ‘ notional’ procedure, triumph over the logician, who troubles 
himself and others with his abstract schemata. But this procedure 
does not abolish a false logic for the sake of a better; it destroys the 
possibility of a methodically progressive logical knowledge of the laws 
of thought. It is only after the investigation, What follows from one 
datum? is finished—that the scientific theory of thinking requires to 
subjoin the consideration of other data. 





298 § 85. Conversion of the 


The given Categorical judgment: All S are P, pre- 
supposes (§ 71) the relations of the two spheres, which 
are signified by the Schema— 


a. i. (s)P 58 


i.e. the action or quality, which the predicate-notion P 
denotes, is (a, 2) found in all the objeets which the 
subject-notion S denotes, while it remains uncertain 
whether it is also found in others (a, 1) or is not so 
found (a, 2). Under the first present position it may 
only be said of part of the objects to which the action 
or quality denoted by the former predicate-notion P 
belongs, that they are S, under the second it may be 
said of all of them. It cannot be decided, from thie 
given judgment alone: All S are P, when other data 
are excluded, which of the two presuppositions holds 
good in any case. But this decision is not required. 
The inference: At least some P are S$, is true on both 
presuppositions. And this is what was to be proved. 
In the same way the hypothetical judgment: When- 





ever Ais, B is, presupposes two relations of spheres, 


whose Schema is— 


i.e. the relation denoted by Β is found everywhere where 
Ais; while it remains uncertain whether it is found mm 


Universal Affirmative Fudgment. 299 





other cases (1), or is not so found (2). But under both 
presuppositions the inference: At least in a part of the 
cases where B is, A is, is equally true. And this is what 
was to be proved. 

There are cases, therefore, where the Converse: All 
P are S, or: Whenever B is, A is, holds good in the 
universal judgment. But at each time a special proof 
is necessary to show that the case before us is such a 
case, and this proof can only be given when other data 
besides the judgment to be converted are present. 
[Cf. Appendix B.] 

Conversion without change of Quantity is called by 
modern logicians Simple Conversion (Conversio Sim- 
plex), Conversion which is accompanied by change of 
Quantity is called Conversion per accidens. These uni- 
versal affirmative judgments, which admit simple or 
pure Conversion, are called reciprocal. 

If the judgment given is only problematically valid, 
or if it is apodictically certain, the same modality be- 
longs to the judgment reached by Conversion. For the 
degree and the kind of the probability or certainty, which 
the given judgment has, must pass over to the judg- 
ment which follows from it. The validity of the second 
is entirely dependent upon the validity of the first. 

Ezxamples.—If the proposition is true: Every true duty 
must harmonise (not only with objective laws but also) with 
one’s own moral consciousness,—the other must also be true: 
Something which harmonises with one’s own moral conscious- 
ness is a true duty, but it does not follow that: Whatever 
harmonises with one’s own moral consciousness is a duty. If 


the proposition is true: Whenever an action is evil in the full 
sense, it must contradict one’s own moral consciousness (or, 








300 § 85. Conversion of the 


If it is evil, it contradicts, &c.); the axiom is also true: In 
some cases (at least), if an action contradicts one’s own moral 
consciousness, it is evil. But the converse does not follow 
for all cases. From the proposition: Whenever the predicate 
in Greek has the article, the spheres of the subject and of the 
predicate-notions coincide with each other, the proposition 
follows: In some cases, at least, where the spheres of the 
subject and predicate-notions coincide with each other, the 
predicate in Greek has the article (in those cases, namely, 
where this coincidence not only exists, but is expressly denoted. 
But it must be known from other data that the converse pro- 
position holds good with this limitation). The validity of the 
converse follows from the given proposition only, ‘in some 
cases, at least.’ We cannot learn from the given proposition 
whether the converse holds good only in some or in all, and if 
true in some only, in what cases. 

Simple convertibility is one condition of the correctness of 
Definitions.! The definition is adequate only when the de- 
finiendum (S) and the definiens (P) are reciprocal notions, and 
have the same extent ; and in this case P can be as universally 
predicated of S, as Sof P. But definitions are not the only 
cases in which universal affirmative judgments admit of simple 
conversion. Almost all geometrical propositions are universally 
true in the converse form; but this must be shown in every 
case by special mathematical proof. It does not follow from 
the logical laws of Conversion. The proposition: All coinci- 
dent triangles have an equal content, can only be converted 
per accidens: Some triangles of equal content are coincident. 
In the same way, the proposition: All parallelograms having 
equal base and height are parallelograms of equal content, is 
to be converted: Some parallelograms of equal content have 
equal bases and height. It must be observed with reference 
to algebraical propositions, that the mathematical notion of 
equality is not identical with the logical copula. The simple 
converse of: All a=b, is not: All b=a, but: Whatever 1s 
equal to B is A. But Logic does not wariant this simple con- 


1 As has already been noticed, $ 62. 


Universal Affirmative $udgment. 301 





version, and mathematical considerations lead only either to 
the proposition: All b=a, or to the proposition: Whatever is 
equal to b, is equal to a. Equal quantities are, with reference 
to quantity, identical; but we cannot make them absolutely 
identical, while the different relations which lie in the different 
expressions, have meaning. 

These rules for Conversion would be false if Herbart’s 
opinion,’ shared by Drobisch? and Beneke, were correct. He 
believes that the truth of the affirmative categorical judgment 
is not conditioned by the actual existence of the object, thought 
in the notion of the subject, but that every kind of judgment 
is valid only hypothetically, on the hypothesis of the se 
tion of the subject. Herbart himself feels the difficulty arising 
from this, but knows better how to state it than to overdone 
it.‘ His example is: The wrath of the Homeric cods—if 
there are any—is terrible. But they are merely nad, and 
have no real existence, and hence, though many a terrible 
thing actually exists, the truth of the converse does not 
follow: Some terrible thing—if there be any—is the wrath of 
the Homeric gods. But, in fact, the truth of the affirmative 
categorical judgment always includes the truth of the hypo- 
thesis, that the object designated by the subject: exists. If 
we refer that assertion about the wrath of the Homeric gods 
to external actual existence, then, because that wrath = 
not exist, it is as false as the converse. But if we allow to 
the world of the Homeric gods an ideal actual existence, both 
the proposition and its converse are equally true in this sda 
and the rules of conversion are warranted to be correct in this 
application also. 

The rules for the Conversion of the Hypothetical judgment 
and their proof enunciated in this and the following ie 
graphs, are correct, only on the hypothesis that the ie 
Ing proposition denotes cases which actually exist. The 
hypothetical proposition expressed by “ Whenever,’ involves 
this hypothesis, just as the categorical judgment involves the 


l > “ . . . 
Lehrbuch zur Einl. in die Phil. § 53. 


Log. 3rd ed. p. 09 ff. 3 Ibid. i. 165. + Lehrb. § 59, Anm. 





302 § 85. Conversion of the 





presupposition of the existence of the subject, provided that 
the nexus does not refer to a merely hypothetical actual exist- 
ence, and the clause ‘if this at all happens’ is not to be added 
in thought. Cf. §§ 68, 94. 

As to Modality, the judgment: All S are P, may be un- 
certain, and yet the judgment: Some P are S, be certain. 
This happens, when it is certain that some S are P, and when 
the uncertainty of the universal judgment refers only to the 
other S. The certainty of the converse follows not from the 
uncertainty of the universal affirmative, but from the certainty 
of the particular affirmative judgment (§ 86), and therefore 
from a datum reached in another way. If we’only know that it 
is uncertain whether all S are P, we are uncertain whether 
some or perhaps none S are P; and it also remains uncertain 
whether some P are S. 

The use of circles as an aid in the demonstration of the 
doctrine of ‘Syllogism, especially in Syllogistic proper, has 
been referred by modern logicians (e.g. by Maass, J. D. 
Gergonne, Bachmann, and Bolzano) to Euler.‘ But Drobisch ἢ 
[and Hamilton *] have rightly remarked that, according to the 
testimony of Lambert,‘ Joh. Chr. Lange, in his “ Nucleus 
Logicae Weisianae,’ 1712, uses circles, and that Christ. Weise, 
rector of the Gymnasium at Zittau (d. 1708 ), (on whose doctrines 
many of the thoughts in this compend are based,) was probably 
the inventor. [According to Hamilton, Lambert’s method of 
‘sensualising the abstractions of Logic’ by parallel lines of 
the different lengths, is to be found in the ‘ Logicae Systema 
Harmonicum,’® of Alstedinos, published in 1614.] Demon- 
stration by means of direct comparison of spheres could only 
come into use after that the authority of the Aristotelian 
methods of reduction had been impugned (more particularly 
by Cartesianism).° These methods prevailed unconditionally, 


I Lettres ἃ une princesse d’Allemagne sur quelques sujets de physique 
et de philosophie, 1768-72, 11. 106. 

2 Log. 3rd ed. p. 96. 

4 Architectonic, 1. 128. 

6 Cf. below, δ 105, 113 ff. 


3 [ Lect. on Log. i. 256.] 
5 EP. 890. 


Universal Affirmative Fudgment. 303 





if we except some attempts at independent proofs among the 
Earlier Peripatetics and by the Neoplatonist Maximus, in the 
latter period of Ancient Philosophy, and during the Middle 
Ages. The ‘ Logique, ou l’art de penser,’? belonging to the 
Cartesian School, teaches certain reductions, but enunciates 
along with them a general principle,? according to which the 
validity of any syllogism may be immediately determined. The 
principle is, that the conclusion must be contained (contenu) in 
one of the premises, and that the other premise must show 
that it is contained, cf. § 120. This thought is not far 
removed from an attempt at a sensible representation by means 
of circles. Among the German logicians Thomasius rejected 
the reductions. The tendency of that age to treat Logic 
mathematically, which Zeibniz was partially influenced by, and 
the didactic requirement of clear and sensible representation, 
may have led to the use of these schemata. 

Prantl* derides, not quite correctly, this sensible represen- 
tation, as serving only to ‘train stupid heads.’ It is, however, 
no more necessarily antagonistic to the consideration of the 
distinetive logical and metaphysical references, and to the 
scientific character of Logic, than the sensible representation 
of geometrical proofs in the figures denoting them need be 
prejudicial to mathematical accuracy. 

Figures of another kind, which represented sensibly only 
the three different positions or fundamental relations of the 
middle notion to the two other notions, in the three Aristotelian 
figures of the Syllogism, were used in Logic in antiquity.° 

Lambert's symbolical notation of the relations of extent 
between the subject and predicate by means of the relations of 
the extent of lines partly continuous partly dotted,® may be 
justified against the accusations of Maass’ and Bachmann.* 

' Cf. Prantl, Gesch. der Log. i. 362, 639. 

* Which appeared in 1662. 

Σ Logique, ou l’ Art de Penser, iii. 10. 4 Gesch. der Log. i. 362. 

° Cf. Barthélemy Saint-Hilaire in the Appendix to his work, De la 
Logique d’ Arist. 1838. 

® Neues Organ. Dian. § 174 ff. 

* Log. p. 142 ff. 


7 Logik, Vorrede, p. 11. 


a 


rom, 
she ὦ utes AN 


Pi 


Rie 7: N 
fad: u ne 


Lu 
ARE PB 





304 § 86. Conversion of the 





They wrongly believe that the mere subordinate reference of 
the upper or under position of the lines is the principal point of 
view. But Lambert’s notation is neither a very easy nor a 
sure way of representation. The notation by triangles adopted 
by Maass is not so convenient as that by circles. 

Gergonne' symbolises the relations of circles by simple 
signs—the identity of two spheres by 1, the complete separation 
by H, the crossing by x, the comprehension of the sphere of 
the subject in that of the predicate by C, and, lastly, the com- 
prehension of the sphere of the predicate in that of the subject 
by o. By the use of these signs the representation attains 
brevity and elegance, but loses immediate intuitiveness. 

[ Mansel objects to the use of any sensible representations 
whatsoever. He thinks that to represent the relation of terms 
in a syllogism by that of figures in a diagram is to lose sight of 
the distinctive mark of a concept,—that it cannot be presented. 
The diagrams of Geometry, he says, furnish no precedent, for 
they illustrate the matter, not the form, of thought. This last 
statement is scarcely correct. 

Hamilton employs, in his Lectures on Logic, the circle 
notation of Euler, and also a modification of Lambert’s linear 
method. The notation (linear) which he afterwards adopted 1s 
very intricate, and while free from the objection that it con- 
founds logical with mathematical extension, does not intuitively 
represent the logical relations.” 

For a history and criticism of various methods of logical 
notation, cf. Hamilton’s Lectures on Logic, i. 256 and 11. 460 ff. | 


§ 86. By Conversion follows— 
I. From the particular affirmative categorical 
judgment (of the form i): Some S are P, 
The particular affirmative judgment (also of 
the form i): At least some P are 5. 


1 Essai de Dialectique rationnelle in the Annales des Mathematiques, 


tom. vii. 189-228, 1816-17. 
[? Cf. Lect. on Logic, ii. Appendix, p. 469 ff., and Discussions, 


pp: 657-661 . | 


Particular Affirmative Fudgment. 305 





And from the particular conditional judgment : 
If A is, B sometimes is, 

The particular conditional follows: Sometimes 
at least if B is, A is. 


The proof results from the comparison of the spheres. 
The given categorical judgment: Some S are P, when 
the predicate P belongs only to sume S, presupposes 
two relations of spheres, which are denoted by the 
Schema :— 


But since the possibility is not excluded, that the 
same predicate P belongs also to other S, the two fol- 
lowing relations of the spheres also exist :— 


These Schemata are to be taken in the same sense 
as in ᾧ 85. Now ini, 1 and i, 3 some P only are §; 
and in i, 2 and i, 4 all, and therefore at least some P 
are δ, But this is what was to be proved. 

In the corresponding hypothetical judgments the rela- 


tions of the spheres are the same and the result equiva- 
lent. 


The Conversion of the particular affirmative and of 
the particular conditional judgment is therefore a Con- 
versio simplex, For both the given judgment, and the 

X 





306 § 87. Conversion of the 





judgment arising from the conversion, take the form of 
the particular affirmative (i). 

The Modality of the given judgment and of its con- 
verse is the same. 


Examples of i, 1 are: Some parallelograms are regular 
figures ;—of i, 2: Some parallelograms are squares ;—of i, 3: 
Some parallelograms are divided by a diagonal into two coinci- 
dent triangles ;—and of i, 4: Some parallelograms are divided 
by both diagonals into two coincident triangles. The relation 
of spheres i, 1 admits of many other modifications. If two spheres 
are of unequal size, it can happen that most S are P, and 
relatively very few P are S, ora few S are P, and most P are ὃ. 
Although the number of S which are P, and of P which are ὃ, 
is in itself necessarily the same, yet the relation of the sum 
total of individuals is a different one in each of the two spheres. 
For example, some, and relatively not a few, planets belonging 
to our system are heavenly bodies which may be seen by us with 
the naked eye; but only a very few of the heavenly bodies 
visible to the naked eye are planets of our system. This con- 
version is not, therefore, conversio simplex, in the stricter sense 
that the quantity remains the same in each reference. It is so 
only in the more general sense, that the judgment remains 4 
particular one, and does not pass over to any other of the four 
classes of judgments designated by 4, @, 1, O. 


§ 87. By Conversion follows— 


III. From the universal negative categorical judg- 

ment (of the form 6): No 8 is P, 

The universal negative judgment (also of the 
form e): No PisS. 

And from the universal negative hypothetical 
judgment: If a is, B never is, 

The similarly universal negative hypothetical 
judgment: If is, A never is. 


Universal Negative Fudgment. 307 





The validity of these rules may be directly proved by 
Th& Schema of the uni- 
versal negative categorical judgment is the complete 
separation of the spheres :— 


the comparison of spheres. 


i.e. The action or quality which the notion of the pre- 
dicate P denotes, is to be found in no object which 
the subject-notion S denotes, and, if it really exists, only 
in other notions. Hence the judgment: No objects in 
which the predicate P is found, and which may there- 
fore be denoted by the notion P made substantive, are S. 
And this is what was to be proved. 

The same may be proved indirectly. For if any one 
P were S, then (according to $ 86) some one 5 would 
be P ; but this is false according to the axiom of Con- 
tradiction (§ 77), for it is opposed contradictorily 
($ 72) to the given judgment: no Sis P. Hence the 
assertion is false, that any one P is S, and it is true that 
no P is 5; which was to be proved. 

The corresponding hypothetical judgment presupposes 
the analogous relation of spheres :— 


ie. The case denoted by B is never found where A is 
present. Whenever B happens, it takes place under 
other conditions. The case B does not occur together 


x2 





308 § 87. Conversion of the 





with the case A; and the case A does not occur with 
the case B. If B is, A never is; which was to be 
proved. 

The indirect proof may be led here as well as in the 
universal negative categorical judgment. For if it once 
happened that when B is, A is also, then (according to 
§ 86) the converse would be true that, once, when A is, 
B is; this would contradict the given presupposition, 
that when A is, B never is, and is therefore false. Hence 
it is false, that when B is, A is once; and the proposi- 
tion is true: when B is, A never is; which was to be 
proved. 

The converse of the universal negative judgment is 
therefore not accompanied with any change of quantity, 
and is throughout simple conversion. 

The rule also holds good without exception that 
Modality remains unchanged in the conversion. If it 
is apodictically certain that no Sis P, the same kind 
of certainty passes over to the judgment, that no P is S. 
If that is only probable, or is true only perhaps, and 
the assertion remains possible, that, perhaps at least 
some one § is P, then (according to ὃ 86) there is the 
same possibility for the assertion that, perhaps at least, 
some one P is S. ‘It does not follow: no P is ὃ; but 
only: Probably or perhaps, no P is S. 


The following are examples of the conversion of the univer- 
sal affirmative categorical judgment. If the judgment be 
given as true: No innocent person is unhappy, it follows with 
equal truth: No unhappy person is innocent. If the proposi- 
tion be proved: No equilateral triangle is ünequiangular, it 
follows without further mathematical demonstration, by logical 
conversion: No unequiangular triangle is equilateral (every un- 


| 
| 
\ 


Universal Negative $udoment. 








equiangular triangle has sides of different sizes). If it is proved 
that: No unequilateral triangle is equiangular, it follows by 
mere logical conversion, that: No equiangular triangle is un- 
equilateral (every equiangular triangle is equilateral). No 
square has a diagonal commensurable with one of the sides ; 
and no figure, with a diagonal commensurable with one of the 
sides, is a square. We may take the theory of parallels as an 
example of the conversion of the corresponding hypothetical 
judgment. The proposition may be proved (it may be known 
without the aid of the eleventh axiom of Euclid): If two 
straight lines (in one plane) are so intersected by any third 
that the corresponding angles are equal to each other, or that 
the interior angles on the same side of the intersecting line are 
together equal to two right angles, these lines will never meet 
in any one point. It follows, by mere conversion, without the 
necessity of going back upon the mathematical construction: If 
two straight lines (in one plane) meet in any point, they are 
never so intersected by any third that the corresponding angles 
are equal to each other, or that the interior angles, on the same 
side of the intersecting line, are together equal to two right 
angles. (In other words: Two angles in any triangle are 
never together equal to two right angles. But it cannot be 
asserted in this way that these two angles together with the 
third make two right angles; nor that, when the intersected 
a not meet, the corresponding angles are equal to each 

Aristotle holds that the universal negative judgment of pos- 
sibility does not admit of altogether simple conversion: "Anal. 
Pr. i. e. iii.: ὅσα δὲ τῷ ὡς ἐπὶ πολὺ καὶ τῷ πεφυκέναι λέγεται 
ἡ δέχεσθαι---- μὲν κωθόλου στερητικὴ πρότασις οὐκ ἀντιστρέφει, 
ἡ δ᾽ ἐν μέρει ἀντιστρέφει" οἴ, c. xiii; c. xvii: ὅτι οὐκ ἀντιστρέφει 
τὸ ἐν τῷ ἐνδέχεσθαι στερητικόν. If the judgment is given: τὸ 
A ἐνδέχεται, μηδενὶ τῷ B, it does not necessarily follow that τὸ 
B ἐνδέχεσθαι μηδενὶ τῷ A. Aristotle understands the first pro- 
position in this sense: Every B, each by itself, is in the state 
of possibility to have or not to have a for a predicate. He 
understands the second proposition similarly, in this sense: 





310 § 87. The Universal Negative Fudgment. 








Every A, each by itself, is in the state of possibility to have or 
not to have B for a predicate (cf. ὃ 98). Now the case may 
occur, as Aristotle rightly remarks, where all B are in that 


double state of possibility, while some A are in the state of 


necessity, not to have B for a predicate. Hence the Schema 
is :— 


In cases of this kind the first judgment (τὸ A ἐνδέχεται μηδενὶ τῷ 
B) is true, and the second (τὸ B ἐνδέχεται μηδενὶ τῷ A) is false. 
Hence the second is not the necessary consequence of the first. 
In this sense Aristotle’s doctrine is well founded. But it does 
not contradict our proposition (which Theophrastus and Eude- 


mus had recognised'), that universal negative propositions of 


any modality, and consequently the problematical, are con- 
verted with Quantity, Quality, and Modality unchanged. The 
contradiction is not overcome by the circumstance that the 
Aristotelian ἐνδέχεσθαι does not denote subjective uncertainty 
like the perhaps of the problematic judgment, but the objective 
possibility of Being and Not Being, more especially (in dis- 
tinction from δύνασθαι) in the sense of there being nothing to 


hinder it. For the argument of Aristotle remains correct, if 


subjective uncertainty be substituted for the objective pos- 
sibility. If it is uncertain of all B, whether they are or are not 
A, it does not follow that it must be uncertain of all a, whether 
they are or are not B. The certainty that they are not B may 
exist of some A. But this does not prejudice the above demon- 
stration that from the proposition: Perhaps no B is A, the 
propesition follows: Perhaps no A is B. For this last prop0- 
sition is not equivalent to that, which can not be deduced: It 
is uncertain of all A, and of each one by itself, whether they 
are or are not B. It is equivalent to the following: It is un- 
certain whether all a are not B, or whether there be at least 


1 Cf, Prantl, Gesch. der Log. i. 364. 


§ 88. The Particular Negative Fudgment. 311 





any one A which is B. And this proposition can very well exist 
along with the certainty that some A are not B. Similarly, 
from the proposition: It is (objectively) possible that no B is A, 
the proposition follows necessarily: It is (objectively) possible 
that no A is B (while it is also possible that at least some one A 
is B). Conversion in the Aristotelian way, according to which 
the possibility not to be B is adjudged to every individual A, 
holds good (as Aristotle himself shows') in two cases — (1) when 
by ἐνδέχεσθαι is understood what might be expressed by it ὁμω- 
yipws: to be at least in the state of possibility, without exelusion 
of the necessity ; and (2) where all necessity whatever is er- 
cluded, and with it necessity in the direction from A to B, 80 that 
no A are present which are in the state of necessity not to be 
Β. The apparent contradiction between the doctrine enun- 
ciated in the text of this paragraph and the Aristotelian is 
solved in this way.? 

§ 88. Nothing follows from the conversion of the 
particular negative judgment. The particular negative 
categorical judgment asserts, that some S have not the 
predicate P, without saying anything definite about the 
rest of S. 


in the three figures :— 
‘ (Or) ᾿ 
: (:) 


or in the one figure, which, comprehending the three 


Its Schema is accordingly the combination 


I Anal. Pr. i. ¢. iii. 2 Cf, Prantl, Gesch. der Log. i. 267, 364. 





312 ὃ 88. The Particular Negative Fudgment. 





possible cases, denotes the definite by the continuous, 
and the indefinite by the dotted lines :— 


According to this, it can happen that when some ὃ 
are not P: (1) Some P are not S, and other P are ὃ ;— 
(2) All P are S; and (3) NoPareS. Nothing can be 
said universally of the relation of P to S in a judgmeat 
whose subject is P. 

Similarly, the Schema of the particular negative 
hypothetical judgment: Sometimes when A is, B 15 not, 
is the following :— 


It may happen that when B is, (1) A sometimes is and 
sometimes is not; (2) A always is, and (3) A never 
is. Hence the general relation of B to A is quite in- 
definite. 


Examples of these different possible cases are the following :— 

Of the particular negative categorical judgments of the form 
1: Some parallelograms are not regular figures. Of the form 
2: Some parallelograms are not squares; or: Some rectilineal 
plane figures, which are divided by a diagonal into two coinci- 
dent triangles, are not parallelograms. Of the form 3: (At 
least) some parallelograms are not trapezoids; or: (At least) 
some rectilineal plane figures, which are divided by a diagonal 
into two triangles not coincident, are not parallelograms. 

Of the particular negative hypothetical judgment of the 


§ 89. Contraposition in general, ete. 313 





form 1: Sometimes, when the accused has confessed himself to 
be guilty, the accusation is not established. Of the form 2: 
Sometimes, when unestablished accusations are raised, there is 
not calumny (only error). Oftheform 3: At least sometimes, 
when the advocate of a higher ideal prineiple is condemned to 
death by the advocates of a principle which is less in accordance 
with reason, but has become an historical power, the right and 
wrong have not been shared equally by both parties. 


$ 89. Contraposition is that change of form, accord- 
ing to which the parts of the judgment change places 
with reference to its relation, but at the same time one 
of them receives the negation, and the quality of the 
judgment changes. Contraposition in categorical judg- 
ment consists in this, that the contradictory opposite of 
the predicate notion becomes the subject, and in this 
transference the quality of the judgment passes over 
to its opposite. In the hypothetical judgment, it con- 
sists in this, that the contradictory opposite of the 
conditioned becomes the conditioning proposition, and 
there is, instead of an affirmative nexus between the 
two parts of the judgment, a negative one, and instead 
of a negative an affirmative one. 

The internal correctness of Contraposition is to be 
decided by the same axioms as that of Conversion 


(cf. ὃ 84). 


The term ‘ conversio per contrapositionem,’ used by Boéthius 
($ 82), where ‘ contrapositio’ means the change of one member 
into its contradictory opposite, is in itself unobjectionable, if 
the notion of conversion is sufficiently widely understood and 
defined. But then a term would be needed to designate the 
first kind of Conversion in the wider sense, or Conversion in 
the stricter sense. Boéthius (cf. § 82) calls it ‘ conversio 





14 § 90. Contraposition of the 
simplex.’ But modern Logic cannot well adopt this term, 
since it denotes by this expression Conversion without change 
of quantity. Hence it is more convenient for us to use the 
notion ‘ conversio’ in the narrower sense only. 

Schleiermacher' adduces the following example of a contra- 
position (‘ Umwendung’): ‘ All birds fly ; not everything that 
flies is a bird’ (instead οἵ: What does not fly is not a bird). 
This, however, rests on a mistake, and not on a peculiar though 
admissible terminology. For the Contraposition, however 
differently in other respects its notion may be defined, must in 
every case fall under the higher notion of immediate conse- 
quence. If the judgment is given: All S are P, the judgment: 
Not all P are S, or: Some P are not S, cannot be derived from 
it by any kind of consequentia immediata. Now Schleiermacher 
himself, in his example, asserts as a new presupposition, the 
perception that other animals fly, and makes this the basis of 


the judgment to be derived. 





§ 90. By Contraposition follows— 
I. From the universal affirmative categorical jJudg- 
ment (of the form a): Every Sis P, 

The universal negative judgment (of the form 
e): No not-P is S (Everything that is not 
P is not 8). 

And from the universal affirmative hypothetical 
judgment: Whenever A is, B is, there fol- 
lows, 

The universal negative: When B is not, A 
never is (It always happens that when B 1s 
not, A is not also). 

Proof may be given directly by comparison of spheres. 
The sphere of P in the categorical, and the sphere of B 
in the hypothetical, jadgment, either includes the sphere 


1 Dial. p. 286. 


Universal Affirmative Fudement. 3 





of S, and that of A, or is exactly coincident with it. 


These relations are to be explained in the same way 
as § 85. In both cases, whatever lies outside of the 
spheres of P and of B, must also lie outside of the 
spheres of S and of A; 1.6. whatever is not P, is also not 
S, and it always happens, when B is not, that A is not; 
which was to be proved. 

The Modality remains unchanged in Contraposition 
in this and in the other forms ($$ 91 and 92), for the 
same reasons as in Conversion. 

The expressions, ‘ contrapositio simplex’ and ‘con- 
trapositio per accidens,’ are used as in Conversion with 
reference to Quantity. 


Examples.—Every regular figure may be inscribed in a circle 
(so that all its sides become chords): Every figure, therefore, 
which cannot be inscribed in a circle is not regular. Every 
rectangular triangle may be inscribed in a semicircle (so that its 
one side becomes the diameter, and the other two chords): 
Every triangle, therefore, which cannot in this way be inscribed 
in a semicircle is not rectangular. Wherever there is a good 
conscience, there will be correct conduct : Wherever, therefore, 
there is not correct conduct, there is not a good conscience. 
Wherever there is perfect virtue, there is also complete internal 
satisfaction: Wherever, therefore, there is not complete internal 
satisfaction, there is not perfect virtue. Every sin contradicts 
the moral consciousness: What does not contradict the moral 
consciousness, is not sin. Whenever the predicate in Greek 
has the article, the spheres of the subject and predicate notions 
coincide : When the spheres of the subject and predicate notions 
do not coincide, the predicate in Greek has never the article. 

The universality with which Contraposition holds good of a 
general affirmative judgment is worth noticing, in opposition to 
the merely particular validity of the judgment reached by con- 
version. Four universal judgments (of the forms ἃ and 6) 





316 ὃ 90. The Universal Affirmative $udgment. 





may always be enunciated, two of which are valid or invalid 
of each other. The first pair may be valid without the second, 
and the second without the first. If the judgment is true: 
Every S is P, it follows that: Whatis not P is not S. But it 
does not follow: Every P is S, nor, what is equivalent to this: 
What is not Sis not P. If the judgment is valid: If a is, B is, 
it follows: If B is not, A is not; but it does not follow: If» 
is, A is, nor, what is equivalent to this; If A is not, B is not, 
For example, if the judgment is recognised to be valid: That 
in which consists the essence of an object is, in its fluctuations, 
the measure of the completeness of the object, the judgment of 
equal universality follows hy Contraposition : Whatever in its 
fluctuations is not the measure of the completeness of an object 
does not contain the essence. But it does not follow; What- 
ever (only some at least) is, in its fluctuations, the measure 
of the perfection of an object contains its essence. Nor does 
the equivalent proposition follow : Whatever does not contain 
the essence of an object, is not in its fluctuations the mea- 
sure of its completeness. (Certain external marks may very 
well fluctuate in strict proportion with the essence.) If the 
proposition is true: Every good thing is beautiful, it follows: 
What is not beautiful is not good. But it does not follow: 
Every beautiful thing is good, nor: What is not good is not 
beautiful. The propositions: Where there is not a very com- 
prehensive memory, there is not a very comprehensive under- 
standing, and: Where there is a very comprehensive under- 
standing, there is a very comprehensive memory, are equivalent. 
But the propositions: Where there is not a comprehensive 
understanding, there not a comprehensive memory, and: 
Where there is a comjrehensive memory, there is a compre- 
hensive understanding, are essentially different from these, 
although equivalent to each other. The two first propositions 
are both true, the two latter are both false. The propositions : 
Whoever does not recognise a state to be independent, does not 
recognise its rights of embassy, and: Whoever recognises the 
right of embassy of a state, recognises also its independence, are 
equivalent. The two following propositions, which are equiva- 


$ 91. The Universal Negative Fudgment. 314 





lent to each other, may be false without detriment to the truth 
of the former: Whoever recognises a state to be independent, 
recognises also its rights of embassy, and: Whoever does not 
recognise the rights of embassy of a state, does not recognise it 
to be independent. (England in 1793 recognised the French 
Republic to be independent, but it did not admit its rights of 
embassy.) In like manner the proposition: Whenever desire 
has gained its utmost height, all pain is removed, admits of 
simple Contraposition, but only of Conversion accompanied by 
change of Quantity. On the other hand a proposition which 
is a definition or corresponds to a definition in this, that the 
spheres of the subject and predicate notions coincide, admits 
both of simple Conversion and of simple Contraposition. For 
example: Every calumny is an untruthful statement of deeds 
which are false and defamatory: Every such statement is a 
calumny ; and: What is not such a statement about such 
deeds (e.g. a false and defamatory account of actions which are 
true) does not fall under the notion of a calumny. 


$ 91. By Contraposition follows— 


Il. From the universal negative categorical judg- 

ment (of the form e): No S is P, 

The particular affirmative judgment (of the 
form i): At least some not-P are S (At 
least something, which is not-P, is 8). 

And from the universal negative hypothetical 
judgment: if A is, B never is, 

The particular affirmative: (At least) in 
some cases, if B is not, A is not. 


For the universal negation both in the categorical and 
in the hypothetical judgment presupposes a complete 
separation of the spheres, and S and a must be found 
outside of the spheres of P and 8 ; i.e. S belongs to what 
is not-P, and A exists in those cases where B is not. 








318 $%92. The Particular Negative Fudgment. 





And so some not-P is S, and in some cases where B is 
not, Ais. The possibility that every not-P is S, or that 
if B is not, A always is, is not excluded; but happens 
only when Sand P, or « and 8, taken in their whole 
extent, include everything existing. 

Examples.—Nothing good is ugly: Something not-ugly is 
good. Nothing ugly is good: Something not-good is ugly. 
No animate essence is lifeless: Something not-lifeless is ani- 
mate. No animate essence is inanimate: (At least) some not- 
inanimate is animate. The divine is not finite: (At least) 
something not-finite is divine. The-finite is not divine: (At 
least) something not-divine is finite. 


§ 92. By Contraposition follows :— 

III. From the particular negative categorical judg- 
ment (of the form 0): (At least) some ὃ 
are not P, 

The particular affirmative judgment (of the 
form i): (At least) some not-P are ὃ (At 
least, something which is not P is 5); 

And in the same way from the particular 
negative hypothetical judgment: (At least) 
sometimes, if A is, B is not, 

The particular affirmative: (At least) in some 
cases, if B is not, A 18. 

For particular negation presupposes, that (at least) 
part of the spheres of S or A lies without the spheres of 
P or 8, without making any definite statement about the 
other part; and so that some of what lies outside of the 
spheres of P or of B, are S or A; 1.6, some not-P are ὃ; 
sometimes, if Bis not, Ais. The case: All not-P are S: 
If Β is not, A always is, may exist, not only when no D 


§93. Zhe Particular Affirmative Fudgment. 319 





is P, and when if A is, B never is (as is possible accord- 
ing to the given judgment) (cf. § 91); it may also occur 
when only some S are not P, and when it only sometimes 
happens that if A is, B is not. The latter case occurs 
more especially when S or A refer to the sum total of all 
existence, and P or B to a part of it. But, whichever of 
these different possible cases exists, anyhow the pro- 
position is true: At least some not-P are S, and: At 
least in some cases, if B is not, A is. 

Examples.—Some parallelograms are not regular figures : 
Something which is not a regular figure is a parallelogram. 
Some parallelograms are not squares: Some not-squares are 
parallelograms. (At least) some parallelograms are not trape- 
zids: Something, which is not a trapezoid, is a parallelogram. 
Some living thing 15. not animate: Something not-animate is 


living. Some real essences are not animate: (At least) some- 
thing, which is not animate, is a real essence. 


§ 93. No conclusion follows by Contraposition from 
the particular affirmative judgment. The particular 
affirmative categorical judgment has, in general, two 
forms (i, 1 and 1, 2), which correspond to the presup- 
position: only some S are P, and two forms (i, 3 and 
i, 4), which correspond to the presupposition: at least 
some, but in fact the other S also, are P. If the 
first two forms were the only ones, it might follow 
(ἡ 92): Some not-P are ὃ. But this consequent has 
no universal validity, because it is not suitable to the 
last two forms. The consequent: (Atleast) Some not-P 
are not S, which contains the proper contraposition, is 
true on the hypothesis of the last two forms, where 
all not-P are also not S ($ 90). It may be applied fre- 





320 § 93. /mpossibility of the Contraposition of 





quently and almost in the greater number of examples 
to the first two forms also. But in case of the first two 
forms, it can happen that it is false. The form i, 2 is 
represented by the figure :— 


It is usually the case that besides the Not-P which are 
S, there are some Not-P which are not S; but it may 
happen that S comprehends the sum-total of existence, 
and then all not-P will be S. It will not then happen 
that there are some not-P which are not S, and that 
consequent will be invalid. The schematic represen- 
tation of the form i, 1 is given in the figure :— 


There are commonly some Not-P which are not δ, be- 
sides the Not-P which are 8, but the opposite case can 
also occur. The form i, 1 (which is distinguished from i, 
3 and i, 4 by the fact that some S are P, and others are 
not, and form i, 2, by the fact that some P are not S) 
exists, when the case represented by the following 
figure occurs :— 


the Particular Affirmative Fudgment. 321 





Where P extends from the centre to the periphery of 
the second circle, and S from the periphery of the first to 
the periphery of the third circle. If the sphere of S is a 
limited one, there will be many not-P which are also 
not S; but if its sphere is unlimited outwards, i.e. if S 
comprehends all existence with the exception of that 
part of P which is denoted by the smallest circle, there 
are no longer some not-P which are not S, but all not-P 
are S. This relation frequently occurs where S is a 
notion designated by a negation (S=Not-I, where I 
stands for the innermost circle) ; and it can also occur 
with an S positively designated. Hence the consequence : 
Some not-P are not S would be false. (The like holds 
good, if in the above figure S and P change places, when 
the sphere of P is unlimited towards the outside.) 

There are cases when the judgment: Some S are P, 
is true, where (at least) some Not-P are S, and there 
are also cases, where No Not-P is S. There are cases 
where (at least) some Not-P are not S, and also cases, 
where all not-P are S. Hence where that one judg- 
ment only is given, nothing can be universally asserted 
of the relation of the Not-P to Sin a judgment whase 
subject is Not-P. 

The corresponding hypothetical judgment, since all its 
relations of spheres are similar, just as little admits any 
universal inversion. 


It is enough to give examples of the two cases where all 
Not-P are S, and where therefore the judgment proves false, 
which would correspond to the universal form of Contraposi- 
tion: Some Not-P are not-S. 1. Some reality is material 
(inanimate). It does not follow from this that: Some thing not- 


2 


Tas Ci as Ψ' Σὼκ Se er , PEE IE nz 
VI ERBE FE 


ET u 


TEN" 
"-" 


BETT 


— | u . 





322 § 93. Lmpossibility of the Contraposition, ete. 











material (psychic) is not real; for every not-material (psychic) 
is real. 2. Some living essences are inanimate. It does not 
follow from this that: Something not-inanimate (animate) is 
not a living essence; for everything which is animate is living. 
The first example corresponds to the form i, 2, where the 
sphere of S extends to the infinite. The second example 
corresponds to that case of i, 1, which is sensibly represented 
by means of the three concentric circles. The inmost circle 
(1) is, in this example, formed by the inorganic or elementary 
essences; the first enclosing ring (A,) embraces plants, and the 
outer ring (A,) animated essences ; P =1+ A, = inanimate 
essences; and S= Not-1= A, + A, = animate essences. 

The proof for the inapplicability of Contraposition to the 
particular affirmative judgment is commonly given in another 
way. The judgment: Some S are P, is reduced to the par- 
ticular negative to which it is equivalent: Some S are Not-P. 
And since the latter cannot be converted (according to the 
laws of Conversion), so the former cannot be transposed.’ But 
this demonstration is beside the mark, unless it is shown that 
the proof of the impossibility of converting the particular 
negative judgment, which is constructed for the case where P 
is a positive notion, holds good for a negative predicate 
Not-P. If this is not specially proved, then that proof may, 
without anything further, be transferred to the case of a nega- 
tive predicate-notion, just as little as in mathematics, e.g., ἃ 
proof, which has been given of a positive whole exponent, 
holds good directly for a negative fractional exponent. The 
transference must obviously submit to a strict test, for the 
whole power of the proof, that PoS does not follow from 
So P, rests on the possibility that in So P the sphere of 5 
wholly comprehends that of P, and that all P are δ. But if 
this relation is found naturally with a positive predicate, its 
possibility is not at all directly evident if the predicate is a 
negative notion and consequently of unlimited extent. The 
doubt rather demands attention, whether this unlimited sphere 
may be completely included by the sphere of S, which, when 


1 Cf. e.g. Drobisch, Log. 2nd. ed. $ 77, p. 56. 


§ 94. Change of Relation. 323 


J 








S is a positive notion, appears to be limited. If it cannot, 
the proof loses its validity for this case, and with it is lost the 
validity of the proof by Reduction of the impossibility of Con- 
traposition in $i P.' 

Twesten says,? ‘ Particular affirmative judgments cannot 
submit to contraposition. If some a are ὦ, it remains un- 
decided whether a is partly or not at all without the sphere of 
b, and partly or not at all within the sphere of not-d.’ This is 
no proof. At the most, it is an introduction to a proof. For, 
from what is given, it follows at once that it is uncertain whether 
some a are not-b, and whether some no#-b are a; it does not 
follow so immediately, that it is also uncertain whether some 
not-b are not-a. And the inadmissibility of the consequence: 
(At least) Some not-d are not-a, is what was to be shown. It 
should have been said: If some a are ὦ, it remains undecided 
whether not-b lies wholly or at least partiy without the sphere 
of a (or, wholly or at least partly within the sphere of not-a). 


§ 94. If in Conversion and Contraposition the posi- 


tion of the individual members of the judgment can be 


1 Drobisch, in the 3rd ed. of his Zogie, ὃ 82, p. 88, has sought 
to show that the proof for the inconvertibility of the particular 
negative judgment holds good for a negative (Not-P) as well as for a 
positive predicate (P); but his proof is not sufficient. He only proves 
that the proposition: Some Not-P are S, cannot be inferred, because 
the case exists in which the contradictory opposite judgment: No 
Not-P is S, is true. What was to be proved, that it cannot be con- 
cluded that: Some Not-P are not S, does not in the least degree 
follow; for this judgment may be recognised to be true when some 
Not-P are S, as easily asit is true when no Not-P are 5. When, accord- 
ing to circumstances, the one or other of two judgments contradictorily 
opposed to each other may be true, it is only implied that neither the 
one nor the other of these two judgments is true in every case. Another 


judgment which coexists with both may be true in every case. Judg- 


ments contradicting each other (No Not-P is 5, and Some Not-P are 
S) may both be uncertain, and a third judgment (Some Net-P are not 
S) may be certain. Drobisch’s reasoning is not sufficient. 
2 Log. p. 79. 
Υ 2 


aT Dr Γ ee “ἦε ὠὰ ἢ - - on 4 o> 
at * σα Se PN Te τα ‘ss 
ab he sei er UNE sil OPA ἢ 





324 § 94. Change of Relation. 











exchanged while their relation remains unaltered, there 
may also be a change in the Relation itself. This occurs 
when an hypothetical is formed from a simple categorical 
judgment (which is always possible), or when several 
hypothetical are formed from a disjunctive categorical 
judgment, or when the converse of both cases happens. 
The possibility of this change of form rests on this :— 

1. The relation of inherence always includes a certain 
dependence of the predicate upon the subject, which 
may always be made conspicuous when it is treated by 
itself, and is expressed in an hypothetical judgment. 

2. The disjunctive judgment is the comprehensive 
expression of several hypothetical judgments, and may 
be resolved into them as easily as these mutually-related 
hypothetical judgments may be reduced to a disjunctive 


judgm ent. 


From the judgment: A is B, the judgment: If A is, B is, 
may be deduced. But the categorical judgment is not always 
correct, when the hypothetical is ; for the latter does not pro- 
ceed upon the hypothesis of the existence of A, but only on the 
fact that B stands in a relation of inherence together with A. 
From the judgment: Every A, which is B, is ©, follows the 
judgment : If A is B, A is C; and the latter, which pre- 
supposes the existence of such A which are B, may be reduced 
to the former. The: judgment: A is either B or c, divides 
into the mutually connected hypothetical judgments: If A is 
B, it is not c, and If Ais C, it is not B; If A is not B, it is 
c,and If ais not c,itisB. And the latter may be again 
reduced to the former. 3 

The possibility of this Change of Relation does not prove! 
that difference of Relation is only verbal, and has no logical οἱ 


1 As several modern logicians believe—viz. Herbart, Einleit. §§ 93, 


60 Rem.; Beneke, Log. i. 163 ff. ; Dressler, Denklehre, 199 ff. 


δ 95. Subalternation. 32 











metaphysical significance. If this view were correct, the 
change of form could be accomplished, without alteration of 
the material constituent parts of the judgment, equally well 
by changing the hypothetical judgment into a categorical as 
by changing the categorical into an hypothetical. But this is 
not the case. The transformation of the hypothetical judg- 
ment into a categorical is only admissible, in so far as a i, 
lation of inherence is connected with the relation of depen- 
dence, and the existence of the subject is ensured, as it is in 
the cases adduced above. It is not possible whenever the 
hypothetical judgment is given: If A is B, c is D; for the. 
fact that A is B does not stand in the same relation to the 
fact that C is D, that A does to B orc does to p. The former 
is not the latter, nor can it be considered to be a kind of 
the latter. But the A zs a B, and can be held to be a kind of 
B. There is not only a verbal, but a logico-metaphysical dif- 
ference, which reveals itself indeed in language, the flexible 
garment or rather the organic body of thought, but belongs 
originally to thought itself. One fundamental.relation suite 
between the parts of the hypothetical judgment, and another 
between those of the categorical. The two are essentially 
related and connected with each other,! but they are not to 
be thought identical. Cf. §§ 68, 85. 


§ 95. Subalternation (Subalternatio) is the passing 

over from the whole sphere of the subject-notion to a 
part of it, and conversely from a part to the whole. 
By Subalternation follows :— 
1. From the truth of the universal categorical judgment 
(8 a Por ὃ 6 P) the truth of the corresponding par- 
tieular (SiP or So P), but not conversely the former 
from the latter. 


| ' Cf. Trendelenburg, Log. Unters. 2nd ed. i. 343; 3rd ed. 351: 
The settled product of causality issubstance;’ 2nd ed. 1.355; 11.246; 
ord ed. i. 863; ii. 270. 


ΡΣ ΟΝ, ΑΓΔ A ERAT ΟΝ 





426 § 96. (Qualitative) A equipollence. 





2. From the falsehood of the particular the falsehood 
of the universal judgment, but not conversely the 
former from the latter. 

The proof for the correctness of the first consequence 
lies in this, that the subalternate judgment repeats an 
assertion lying in the subalternant, and only asserts as 
true what is already recognised to be true. The second 
consequence is founded on this, that, if the universal 
judgment be true, then (according to 1) the par- 
ticular is true, which contradicts the hypothesis. The 
converse consequences, however, are not universally 


valid, because the truth of the particular judgment may | 


co-exist along with the falsehood of the universal, be- 
cause it may happen that Some S are and others are 
not P. 

The same laws hold good of hypothetical judgments 
(If A is, B always is—At least in some cases, if A is, B 
is also). 

The consequence from the universal to the particular 
is called consequentia or conclusio ad subalternatam pro- 
positionem, that from the particular to the universal con- 
clusio ad subalternantem. 

The older logicians were accustomed to express the law of 
consequence, ad subalternatam propositionem, in the dictum de 
omni et nulle, in the following way: ‘ quidquid de omnibus 


valet, valet etiam de quibusdam et singulis ; quidquid de nullo 
yalet, nec de quibusdam vel singulis valet.’ 


§ 96. By (qualitative) AEQUIPOLLENCE (aequipollentia) 
modern Logie means the agreement in sense of two 
judgments of different Quality. This agreement becomes 
possible by the fact that the predicate notions stand in 


§ 96. (Qualitative) Aeguipollence. 


ed. 
Re Ta 





the relation of contradictory opposition to each other. 
Consequence per aequipollentiam proceeds from the 
judgment: All S are P, to the judgment: No S is not-P, 
and vice versä; from the judgment: No S is P, to the 
judgment: Every S is a Not-P, and vice versä; from 
the judgment: Some S are P, to the judginent: Some 
S are not Not-P, and vice versä ; and lastly from the 
judgment: Some S are not P, to the judgment: Some S 
are Not-P, and vice versa. 

The proof for the correctness of these consequences 
lies in the relation of the spheres, according to which 
every S, which does not fall within the sphere of P, is 
outside it, and must lie in the sphere of Not-P; and 
whatever falls within this cannot lie within the sphere 


of P. 


Every sin contradicts the conscience; there is no sin which 
does not contradict the conscience. Nothing sinful is in 
harmony with the ethical consciousness; whatever is sinful is 
not in harmony with the ethical consciousness, 

The earlier logicians' understand by ἐσοδυναμοῦσαι προ- 
Tages, indicia aequipollentia sive convenientia, every kind of 
equivalent judgments, i.e. those which with material identity 
are necessarily true or false together because of their form. 
(Cf. the expression ἀντιστρέφειν found in Aristotle.?) 

Kant? and some modern logicians with him will not allow 
the inferences of Aequipollency to be inferences proper, 
because there is no consequence, and the judgments remain 
unchanged even according to form. They are to be looked at 
only as substitutions of words which denote one and the same 
notion. But since in Aequipollency the Quality of the judg- 


ı Cf. § 82. 2 De Interpret. e. xiii. p. 22 A, 16. 
3 Log. ed. Jäsche, ὃ 47, Rem. 


2 or - bas . . a 
SITE ii sie ay ae En ? 
δῶν, ἃ 





328 δ΄ 97 Opposition. 








ment passes over to its opposite, however trivial the change 
may be which here exists, it evidently concerns the form of 
the judgment itself, and not its mere verbal expression. 


§ 97. Opposition (oppositio) exists between two judg- 
ments of different Quality and different sense with the 
same content. 

By Opposition follows (cf. §§ 71 and 72) :— 

1. From the truth of one judgment the falsehood of 
its contradictory opposite, since according to the axiom 
of contradiction (§ 77) judgments opposed contradic- 
torily cannot both be true ; 

2. From the falsehood of a judgment the truth of its 
contradictory opposite, since according to the axiom of 
Excluded Third ($ 78) judgments opposed as contra- 
dictories cannot both be false ; 

3. From the truth of one judgment the falsehood of 
the contrary opposite (but not conversely from the false- 
hood of the one the truth of the other), according to the 
axiom that judgments opposed as contraries cannot both 
be true (though both may be false). Otherwise the 
assertions opposed as contradictories, which (according 
to § 95) are contained in them and may be deduced by 


Subalternation, must both be true, and the axiom of | 


Contradiction does not admit this (but their common 


falsehood includes neither the truth nor the falsehood of | 


assertions which are opposed to each other as contra- 
dictories ) ; 

4, From the falsehood of a judgment the truth of its 
subcontrary (but not conversely from the truth of the 
one to the falsehood of the other), according to the 
axiom, that subcontrary judgments cannot be both false 


N 07. Opp- sehon. | 329 





(but may both be true), because otherwise (according 
to 2) their contradictory opposites, which stand to each 
other in the relation of contrary opposition, must both 
be true, and also (according to 3) cannot both be 
true. 


According to 1, there follows by an inference ad contradic- 
toriam propositionem. 


From the truth of S a P, the falsehood of So P; 
From the truth of Se P, the falsehood of 5 1 P; 
From the truth of Si P, the falsehood of Se P; 
From the truth of S o P, the falsehood of S a P. 


According to 2, there follows by an inference ad contradic- 
toriam propositionem :— 


From the falsehood of S a P, the truth of So P; 
From the falsehood of Se P, the truth of Si P; 
From the falsehood of Si P, the truth of Se P; 
From the falsehood of S o P, the truth of S a P. 


According to 3, there follows by an inference ad contrariam 
propositionem :— 
From the truth of Sa P, the falsehood of Se P; 
From the truth of S e P, tke falsehood of S a P. 


According to 4, there follows by an inference ad subcon- 
trariam propositionem :— 
From the falsehood of Si P, the truth of So P; 
From the falsehood of So P, the truth of S 1 P. 


The like consequences hold good in the corresponding hypo- 
thetical judgments. | 

Although the transformations given in this paragraph are so 
simple that they seem to need no examples or illustration, yet 
one may be given to show that attention should be paid to 
these relations not merely for the sake of logical theory, but 
also for their practical application, which is not unimportant. 
The truth of the affirmation is equivalent to the falsehood of 





§ 97. Opposition. 








the negation, and the truth of the negation to the falsehood of 
the affirmation. Affirmation is opposed to ignorance, inat- 
tention, or negation. Negation is (according to § 69) only. 
suitable where a motive for affirmation can at least be thought, 
and more especially where an affirmation has actually been 
made by others. Hence in the interpretation of an affirmation 
the sense of the negation must be kept in mind, and in the 
interpretation of a negation the content and form of its cor- 
responding affirmation. According to this rule, if Heinrich 
Diintzer’s conjecture! in Hor. Epod. v. 87, ‘ venena magna,’ be 
accepted, an explanation different from Diintzer’s must be 
given. Duntzer translates: ‘Strong.charms may perpetrate 
intentional transgression; they cannot change a man’s condi- 
tion’ But the first part of this sentence (if we suppose that 
Horace expressed these thoughts by these words) is languidly 
directed against the witches. The negation which in the natural 
construction refers to the whole of the sentence is opposed to 
an affirmation made by the witches. They believe that a 
change in human nature (convertere humanam vicem, the 
change from hate or indifference to love), unattainable by 
weaker charms, may be brought about by stronger (venena 
magna); and they believe those charms to be strong (as Dun- 
tzer remarks) for whose preparation crimes are necessary. But 
they have not avowed to themselves nor to others the whole 
nefas; the fear of the knowledge of the crime still remains to 
some extent, even when the fear of the crime itself has 
departed ; and so the perpetrators assure themselves and others 
that the scrupulous distinction between fas and nefas vanishes 
only in ‘more potent’ means, and that in means of that kind 
fas and nefas are equivalent. They declare: venena magna 
(ac?) fas nefasque (i.e. venena magna per fas nefasque adhibita ) 
valent convertere humanam vicem; and the boy whom they 
threaten denies this assertion. The truth of the negation 
which he asserts is equivalent to the falsehood of what the 


witches affirm. 
1 Philol. xxvii. 184. 


§ 98. Modal Consequence. 31 





§ 98. MoDAL CONSEQUENCE (consequentia modalis) is 
change of modality. By modal consequence follows 
(cf. § 69) :-- 

1. From the validity of the apodictic judgment the 
validity of the assertorical and of the problematic, and 
from the validity of the assertorical, that of the pro- 
blematic judgment; but from the validity of the pro- 
blematic that of the assertorical and apodictic does not 
conversely follow, ner from the validity of the asser- 
torical that of the apodictic ; 

9. From the inadmissibility of the problematic judg- 
ment follows that of the assertorical and apodictic, and 
from the inadmissibility of the assertorical that of the 
apodictic judgment; but from the inadmissibility of the 
apodictic judgment does not follow conversely that of 
the assertorical and problematic, nor from the inad- 
missibility of the assertorical that of the problematic 
judgment. 

The first consequence depends (in the same way 
as Subalternation) on the fact that the judgment de- 
duced only repeats a moment which is contained in 
the given judgment. Apodictic certainty, when we 
abstract the reason of the certainty, justifies us in 
stating the judgment in its assertorical form, as simply 
true, and therefore still more in attributing to it at 
least probability. In the same way the immediate cer- 
tainty which the assertorical judgment expresses, in- 
cludes probability as a moment. On the other hand, 
the certainty of the higher degree is not conversely con- 
tained in that of the lower degree. 

The second consequence rests on this, that where the 





§ 98. Modal Consequence. 











lower degree of certainty is wanting, the higher must 
also be absent. On the other hand, it is not to be 
concluded conversely, that, where the higher degree is 
not present, the lower must also be absent. 


Since Modality treats of the degree of (subjective) certainty, 
the terms: validity or admissibility, and invalidity or inad- 
missibility, must be used, and the notion of truth or falsehood 
must not be unconditionally substituted for them. For example, 
if the assertorical judgment: A is B, is inadmissible, the reason 
may consist in this, that we have not the (subjective) con- 
viction of its truth, while the judgment in itself may be 
true. In this case the problematic judgment: A is perhaps 
B, may remain thoroughly admissible or valid. But if the 
assertorical judgment: A is B, is false, then according to the 
axiom of Excluded Third (§ 78) its contradictory opposite: A 
is not B, is true; and if this is once established, the problematic 
judgment: A is perhaps B, is no longer correct. 

The same postulate holds good in this relation which is true 
of the particular judgment, that the assertion of the less (there 
of some, here of perhaps, &c.) is to be understood not in the 
exclusive sense (only some, only perhaps, &c.), but in the sense 
of containing the possibility of the greater (at leust some, at 
least perhaps). 

Analogous laws are valid with reference to objective possi- 
bility, actuality, and necessity, but their explanation belongs 
rather to Metaphysics than to Logic. Aristotle has treated of 
them in his logical writings, especially in De Interp. c. xii. He 
finds a difficulty in the question, whether possibility follows 
from necessity. On the one hand, it appears to do so. For if 
it were false that what is necessary is possible, it must be true 
that what is necessary is impossible, which is absurd. But on 
the other hand, it appears that the proposition must also be 
valid: What has the possibility to be has also the possibility 
not to be, and so what is necessary, if it were something pos- 
sible, would have a possibility both to be and not to be, which 
is false. Aristotle solves this difficulty by the distinction, that 








§ 99. Mediate Inference. Syllogism and Induction. 333 


the notion of the possible is used partly in a sense in which 
necessity is not excluded (at least possible), in which sense it 
may be applied to those energies which include the dynamis, 
partly in a sense which excludes necessity (only possible), in 
which sense it may be applied to the dynamis which are not 
energies. In the former sense the necessary is a possible, in 
the latter it is not. (In reference to possibility in the nar- 
rower sense, which excludes necessity, Aristotle says! that the 
μὴ ἐνδέχεσθαι, since it denies possibility on both sides equally, 
finds application not merely where the thing is impossible, but 
also where it is necessary.) Later logicians, since they appre- 
hend the judgment of possibility according to the analogy of 
the particular, and accordingly presuppose the meaning: at 
least possible, enunciate the rule: ‘ab oportere ad esse, ab 
esse ad posse valet consequentia: a posse ad esse, ab esse ad 
oportere non valet consequentia.’ 


$ 99. MEDIATE Inrerence divides into two chief 
classes: Syllogism in the stricter sense (ratiocinatio, dis- 
cursus, συλλογισμός), and Induction (inductio, ἐπαγωγή). 
Syllogism in the stricter sense, in its chief forms, is in- 
ference from the general to the particular or individual, 
and in all its forms inference proceeding from the 
general. Induction is inference proceeding from the 


individual or particular to the general. Inference by 


Analogy, which proceeds from the individual or parti- 
cular to a coordinate individual or particular, is a third 
form distinct from both, though able to be reduced to 
a combination of the other two. 


If it is proved universally that only two tangents can be 
drawn to any conic section from one and the same point, and 
it is then inferred: The Hyperbola is a conic section, for this 
proposition holds true of it, the reasoning is a Syllogism. But 
if, on the contrary, it is first shown of the circle, that from one 


I Analyt. Pr. i. 17. 


u » .* 
ai ogre Ds 
wu nn eye ee ee 





334 §99. Mediate [nference. Syllogism and Induction. 








and the same point only two tangents can be drawn to its cir- 
cumference, and then the like is inferred of the ellipse, para- 
bola, hyperbola, and it is concluded: this proposition holds good 
of all conic sections whatever, the reasoning is an Jnduction. 

Kepler and his followers proceeded inductively in the esta- 
blishment of the laws named after him, for they generalised the 
truth of the results proved of Mars, and extended them to the 
other planets. But the converse procedure accomplished by 
Newton is syllogistic; for he proved, on the ground of the 
principle of gravitation, that every planet must move round its 
central body, or rather round the common centre of gravity, 
in a path which is a conic section, and such that the radius 
vector sweeps over equal areas of the plane of the orbit in equal 
times, and that when several bodies move around the same 
centre of gravity, the squares of their periods must be pro- 
portional to the cubes of their mean distances; and he applied 
these axioms td planets, moons, and comets. The molten con- 
dition of the interior of the earth is proved inductively from 
the connection of volcanic phenomena, deductively or syllogis- 
tically from the process of the earth’s formation (probable on 
astronomical grounds). 

The Syllogism in reference to its most important and, for 
positive knowledge, most productive forms, may be called 
‘ the inference of subordination’ (with i Hoppe,' who also calls 
it ‘inference by analysis of notions’); Induction (with Hoppe), 
the ‘ inference of superordination;’ and inference by Analogy 
(Hoppe does not recognise Analogy as a special form), * in- 
ference of coordination.’ ? 


1 Die gesammte Logik, i. Paderborn, 1868. 

2 The remarks made above (§ 84) upon Hoppe’s charge of schema- 
tism in the logical treatment of immediate inferences may be repeated 
of what he calls the ‘schematic and mechanic procedure’ of Syllogistic. 
If it is supposed that over and above the given judgment we know the 
particular kind of knowledge involved, the particular kind of union of 
predicate with subject, and which of the different relations of the pre- 
dicate with the subject actually exists in the individual case, then of 
course more may be concluded than is admissible according to the 
‘schematic procedure ;’ but the number of the legitimately presupposed 
data has been exceeded. 


335 


§-100. Szmple and Complex Syllogism, etc. 





The Syllogism has ever experienced much childish trifling 
at the hands of its advocates, and much perversity from its 
opponents. But he who fairly compares both, will find the 
greater misunderstanding on the side of the opponents. Its 
advocates possess at least a certain degree of acquaintance 
with the matter, while many of its opponents, with equal 
ignorance and arrogance, abuse what they do not under- 
stand. 


$ 100. The syllogism is smMpLE (simplex ), when from 
two judgments, which are different and have a common 
element, a third judgment is derived. It is COMPOSITE 
(compositus), when more than three elements of judg- 
ments, or more than two judgments, serve to establish 
the conclusion. The common element mediates the 
inference, and is accordingly called the middle (medi- 
ating) notion or middle term (medium, terminus medius, 
nota intermedia, τὸ μέσον, ὕρος μέσος). It comes, as the 
name tells, into each of the premises, but not into the 
conclusion. The given judgments, from which the new 
one is derived, are called premises (propositiones prae- 
missae, iudicia praemissa, posita, προτάσεις, τὰ προτεινό- 
μενα, τὰ τεθέντα, τὰ κείμενοι, also sumptiones, accepti- 
ones, λήαματα), and the judgment deduced, the conclu- 
sion (conclusio, iudicium conclusum, illatio, συμπέρασμα, 
ἐπιῷορά). The one premise, which contains the sub- 
ject, or the subordinate propositional member (e.g. the 
hypothesis) of the conclusion, is called the Minor Pre- 
mise (propositio minor, assumptio, πρόσληψις); the 
other, which contains the predicate or the superordinate 
propositional member (the axiom or principal sentence), 
is called the Major Premise (propositio major, λῆμμα). 





336 $ 100. Simple and Complex Syllogism, ete. 





The component parts of the syllogism or the members of 
the judgments contained in it, are comprehended under 
the name, Elements of the Syllogism (Syllogismi Ele- 
menta, Ta τοῦ συλλογισμοῦ στοιχεῖα). The Relation of 


the syllogism is determined by that of its premises, 1.6, 
the syllogism is copulative, disjunctive, hypothetical, &c., 
or mixed, according to the form of the premises. If the 
premises are of different forms, the Relation of the 
Syllogism should, by preference, be that of the Major 


Premise. 


From two judgments, which have nothing in common, no 
new relation can be established, and no conclusion deduced. 
If a third follows from two judgments, they must either have a 
common element, or can receive it by a mere change of form. 
The latter case exists, when one element of the one judgment 
is the contradictory opposite of an element of the other. This 
case can be enumerated among simple syllogisms only if the 
notion of such syllogism be defined in this way, that every 
syllogism which is founded on two given judgments inde- 
pendent of each other, without a third not produced by a mere 
change of form being brought in, is to be called simple; and 
that that only is compound which presupposes more than two 
judgments given. But in the course of exposition this defini- 
tion would lead to many mistakes. Several of the rules which 
syllogistic must enunciate (e.g. the axiom: ex mere negativis 
nihil sequitur, cf. § 106; the statements about the number 
and form of the valid moods, &c.) would not hold good, and 
would require to be superseded by others less simple and 
evident. In internal correctness also this terminology would 
be inferior to that enunciated in the text of this paragraph. 
For in the case, when two elements of the two premises stand 
to each other in the relation of contradictory opposition, the 
conclusion cannot be reached unless a judgment which follows 
by aequipollence from one of the given judgments is added in 


thought. Hence the inference is actually compound,—com- 





N ἊΣ ; U 
191. Syllogesm as a Form of Knowledge, etc. 3 37 


pounded, viz. of an immediate consequence and a simple syl- 
logısm. 
. . “ . 

The expressions ὅρος and πρότασις are explained by Aristotle.! 
He also defines the middle notion (τὸ μέσον). The name 
συμπέρασμα is often found.* The terms λήμματα and ἐπιφορά 
belong to the Stoics. 


§ 101. The possibility of the syllogism as a form of 
knowledge rests on the hypothesis, that a real conforma- 
bility to law exists, and can be known, according to the 
axiom of Sufficient Reason (§ 81). Perfect knowledge 
rests on the coincidence of the ground of knowiadine 


with the real cause. Hence that syllogism is most 


valuable, in which the mediating part (the middle notion, 
the middle term), which is the ground of the knowledge 
of the truth of the conclusion, also denotes the real cause 
of its truth. 


| The doctrine stated in this paragraph is the most important 
in the whole of syllogistic. The decision of its most important 
question of debate depends on the reference in the syllogism 
toa real conformability to law. Is the syllogism a mean to 
knowledge, and is it to be set side by side with the notion and 
judgment as a form equally correct in this sense, or is syllo- 
gistic procedure to be reckoned a mere combination of notions, 
which may perhaps serve to give greater clearness to the 
knowledge we already possess in an undeveloped way, and 
may have some worth for the purpose of communicating our 
knowledge to others? If the conviction of the ey 
valid truth of the premises is not founded on the presupposition 
of a real conformability to law, but is first reached by com- 
parison of all individual cases,—then it is evident that those cases 
which are asserted in the conclusion must also be included in 
the cases compared, that the truth of the conclusion must 
already be established ere the truth of the premises can be 


I Anal. Pri. i. 1. 2 Ibid. i. 4. 3 Ibid. i. 9. 
L 





Zu 


.---------ε«  -οΟ-..--- ---- -- 


338 δϑιιοι. Sylogısm as a Form of Knowledge. 





recognised, and that we really fall into the fallacy of the Circle 
when we attempt again to deduce the conclusion from the 
premises. This last deduction can, at most, have the value of 
a ‘deciphering of our notes’ (Mill), and can serve only to 
recall to our recollection, to make clear, or to communicate to 
others. And in fact, syllogistic does no more in many Cases. 
For example, if the syllogism is enunciated: Every body 
describing an elliptical orbit round our Sun is of itself a dark 
body; Vesta is a body describing an elliptical orbit round our 
Sun; therefore Vesta is in itself a dark body,—it is evident 
that I can recognise the universal validity of the premises only 
when I know that Vesta belongs to the bodies describing an 
elliptical orbit round our Sun, and that it possesses no light of 
‘ts own. So little can I know the truth of the conclusion from 
the truth of the premises, that, on the contrary, the conviction 
of the truth of the first premise must be founded on the pre- 
viously established conviction of the truth of the conclusion, 
and that if the conclusion is shown to be uncertain or false, the 
first premise shares the same fate. The proposition, that all 
planets are always seen within the zodiac (which is true of all 
the planets known to the ancients) loses its apparently universal 
validity, so soon as any one is found (among the asteroids) 
which passes beyond the zodiac. _ It cannot be inferred from 
the general proposition, as if this proposition were established 
previously to and independent of a complete enumeration of 
the particulars, that there can be no planet which passes 
beyond these limits. The planet Pallas actually passes beyond 
them. But all cases are not of the same kind. So far asa 
definite conformability to law can be established with reference 
to any relation to be explained, the universal may be recognised 
to be true before a thorough investigation of the sum total οἱ 
all the individuals, and therefore the truth of the individuals 
ean be arrived at from its truth by syllogistic deduction. For 
example, since Newton’s time we can know that the laws of 
Kepler have universal validity, without first “testing their 
application to all planets and satellites, and whenever a new 


body of this kind is discovered, those laws may be syllogis- . 


tically applied to it with perfect assurance. The certainty οἱ 


Its Relation to the Real Reign of Law. 


39 





the laws derived from the principle of gravitation is so firml 
established, that when the observed orbit of Uranus appeared “4 
contradict them, this observation did not raise an objection to 
their certainty ; it rather justified the inference of the presence 
of some planet hitherto unobserved, and affecting this orbit,— 
an inference which led to the discovery of Neptune. In di 
way, in all cases in which our thinking rests on the foundation 
of a definitely known real conformability to law, the syllogism 
is a completely correct form of knowledge, to which we ‘oul 
valuable extensions of science. 

If the middle term in a syllogism which makes a real addition 
to our knowledge is the expression of the real cause, it must not 
be forgotten that the real cause can only accomplish the effect 
in combination with the corresponding external conditions. For 
example, in the inference: What lengthens the pendulum 
increases the times of its swing; Heat lengthens the pendulum, 
and so increases the times of its swing,—the lengthening of 
the pendulum by heat is the real cause of the increase of ‘the 
time of its swing, but is so only because of the attraction 
of the earth and the motion of its parts according to the 
laws of the case. Cf. § 69, and § 81, upon the combi- 
nation in every cause of the (internal) ground and (external) 
conditions. 

Aristotle expresses the doctrine stated in this paragraph with 
perfect distinctness when he demands that the middle term 
must express the real cause:! τὸ μὲν yap αἴτιον τὸ μέσον. 
Aristotle does not here ‘ trace the real back to the formal,’ as 
Drobisch says,” but conversely gives depth to the formal by 
showing its reference to the real. For although the expression 
quoted admits of two meanings, because both subject and 
predicate have the definite article, and the sentence is re- 
ciprocal, only one meaning corresponds to the context. In 
order to be sure of existence, says Aristotle, and in order to 
recognise essence, we must have a middle term. If we have 
this, we know the cause, and have found with it what was 


1 / hi > € 
Anal. Post. ii. 2, 90 a, 6. 2 Log. Pref. 2nd ed. p. xi. 





40 § τοι. Syllogism as a Form of Knowledge. 


“ 
2 








especially sought, and what we must seek ; for the certainty 
of the (real) cause evidently ensures the certainty of the 
existence. And the meaning of our proposition is: The signi- 
ficance of the middle term lies in this, that it corresponds to 
the cause.! The opposite thought: The essence of the αἴτιον 
lies in this, that it is the middle term of an inference, would 
not correspond to the context. For from the propositions : 
the αἴτιον ensures the existence, and: the essence of the αἴτιον 
lies in this, that it is the middle term of an inference, what 
Aristotle wishes to prove, that whenever we have the middle 
term the existence is ensured, would not follow. It would 
be a fallacious universal affirmative syllogism in the third 
figure. Waitz says in his Commentary:? ‘ Quum omnis 
quaestio iam in eo versetur, ut rei subiectae naturam sive 
causam, per quam res ipsa existat vel ob quam aliud quid de 
ea praedicetur, exploremus, quam quidem causam terminus 
medius exprimere debet. The examples, which Aristotle 
adduces here and in other passages, show that he does not 
mean to resolve the real into the formal, but to comprehend 
the form in its relation to the content. The real ἀντίφραξις of 
the earth between the sun and the moon is the αἴτιον of the 
eclipse of the moon. Now it is evident that the essence of that 
real position of heavenly bodies with regard to each other does 
not lie in this, that it is the middle term of a syllogism, but on 
the contrary, the essence of the middle term lies in this, that it 
denotes the real cause. (An opaque body which comes between 
a luminary and a body, which, dark in itself, is light by means of 
the other, causes an eclipse of the latter. The earth is an opaque 
body, which at certain times comes between the luminary, the 
sun, and the moon which is dark in itself and made luminous by 
the sun. Hence at certain times the earth causes an eclipse of 
the moon.) In the same sense Aristotle teaches® that the four 


1 This does not conflict with what Aristotle says (Anal. Post. ii. 12, 
init.): τὸ yap μέσον αἴτιον. Becoming and having become, &c., have 
the same mean; but the mean is the cause,—therefore they have the 


same cause. 
2 Ad Anal. Post. ii. 2, 580. 3 c.xi. 


Its Relation to the Real Reign of Law. 341 





metaphysical airiar: Essence, Condition, Movine Cause, and 
Final Cause, are all denoted by the middle kn and EN to 
be so denoted, not because they are all reduced to a single 
formal reference, and their real metaphysical character dic: 
stroyed, but, on the contrary, because the real reference of the 
metaphysical αἰτίαι is represented in the middle term. Aristotle 
remarks,’ that in what actually happens, there is partly a strong 
causal necessity and universality, but partly only an os bri 
τὸ πολύ, and adds: τῶν δὴ τοιούτων ἀνάγκη Kal τὸ μέσον ws ἐπὶ 
τὸ πολὺ εἶιαι. The nature of the middle term is evidently 
determined by the nature of the case, the ‘ formal’ by the 
‘real,’ and not conversely. The Aristotelian postulate, that 
(human ) thinking must conform to existence, proceeds also 
upon this. It was reserved for a modern philosopher, Kant 
despairing, in consequence of so many failures made by bie. 
matic philosophers, of establishing a knowledge of ‘ ἀβορεῖο. 
themselves,’ to grasp the converse principle, that the Hak (the 
world of phenomena) must adapt itself to the forms of our 
Tune aut tack to da heen” dhqaits elias taie al 

a. J its that there 
are also syllogisms, in which the actual cause is not. appre- 
hended, and that the effect, because it falls within sense-per- 
ception and is therefore able to be known by us, serves for the 
middle term, and that we infer back from this to what causes. 
W e may do this when the effect can have one cause only, and 
the judgment, in which the causal-nexus is thought, is there- 
fore to be converted simply—avrıorpedov.” He refers the fol- 
lowing example to this last case: What does not twinkle is near; 
the planets do not twinkle, therefore they are near. But syllo- 
gisms of this kind are of less value and are not valid in the most 
strictly scientific manner. The scientific or apodictic syllogism 
must derive the conclusion from the true and proper ea 


1 


: 2 Anal. Pr. i. 18. 

ΞΞ Anal. Post. i. 2,6, and passim. Drobisch says in the third edition 
of his Logic, p. 170, that the Aristotelian axiom, τὸ αἴτιον τὸ μέσον, 
appears to have the meaning, that when the syllogism is applied to real 


c. xil. pr. fin. 


τυ . 
QO; ere + - . 
jects, the middle notion has the meaning of cause, or the cause 15 





342 $ 101. Syllogism as a Form of Knowledge. 





In so far as the true and proper ground of a thing lies in its 
essence (οὐσία or τί ἐστι), to this extent the syllogism rests upon 
the essence,! and since the definition gives the essence, syllo- 
gistic knowledge stands in the most intimate reciprocal relation 
to knowledge by definitions, in spite of their undeniable dif- 
ference. The definition is the principle of the syllogism in so 
far as it supplies the major premise, and the syllogism leads to 
definition in so far as its middle notion reveals the essence in 
the cause.” 

Later logicians, and among them the Stoves, neglected to 
refer the middle term to the real cause, and syllogistic thinking 
generally to the real conformability to law, and confined their 
attention too exclusively to the easier technical parts of the 
Aristotelian syllogistic. Hence we need not wonder that the 
Sceptics of antiquity combated the syllogistie procedure in 
general by the assertion, which has often been repeated in 
modern times, that the premises so far from being able to 
establish the truth of the conclusion, presuppose it. Sextus 
Empiricus*® says that the major premise can only be made 
certain by induction, and that induction presupposes a com- 
plete testing of every individual case; for a single negative 
instance (the crocodile moves not the under, but the upper 
jaw) can destroy the truth of the. universal proposition (all 
animals move the under jaw). On the other hand, if the test- 
ing has completely included every individual member, we 


known by it, but not that it is the cause. It seems to me that, ac- 
cording to Aristotle, the middle notion (is not, but) expresses the real 
cause and corresponds to .it, that the cause is recognised by it. 
But I cannot appropriate the expression that the middle term, 
in its application to the real, receives the meaning of cause. Since the 
middle term brings the real cause (independent of it and existing before 
it), or as Drobisch says, the ‘chief cause,’ within our knowledge, it 
follows that in a syllogism of this kind the ‘ formal,’ or the manner of 
knowing, is conditioned by the ‘real,’ or the objective causal relation. 
This holds good also in mathematical inferences. 

1 Metaph. vii. 9, ὃ 7, ed. Schw. 

2 Anal. Post. i. 8; ii. 3, sqq.; De Anima, ii. 2, 

3 Pyrrhon. Hypotyp. ii. 194 fi. 


Its Relation to the Real Reign of Law. 343 





argue in a vicious circle, when we deduce the individual from 
the universal syllogistically. 

In modern times it has often been made a matter of reproach 
against the logicians of later antiquity, and of the Middle 
Ages, that they have spun out with great subtlety the technical 
part of the Aristotelian logic. It must be admitted that the 
charge is justifiable, inasmuch as they, wholly devoted to the 
technical, let the deeper elements pass unobserved. But it is 
intolerable in the mouth of those who do not regard the rela- 
tions of the formal to the real any more than the Schoolmen did, 
and seek their own renown and pre-eminence over them only 
because they disdain and neglect the technicalities of their 
science. Is the superficiality and heedlessness, which in mo- 
dern times has become only too frequent (many logical text- 
books especially, especially from the Kantian period, swarm 
with logical blunders), to be preferred to the Scholastic accuracy 
and acuteness? Or does not exactness in these matters, as in 
everything, deserve praise? The very didactic artifices of the 
Schoolmen, although we look on them as trivialities, deserve at 
least excuse, because they serve their immediate purpose so 
well. The mathematician Gergonne says rightly :' ‘ Le grand 
nombre de conditions auxquelles on avait cherché a satisfaire 
dans la composition de ces vers artificiels (dont chaque mot 
rappelait une des formes syllogistiques concluantes), aurait 
peut-étre dü en faire excuser un peu la dureté qui a été dans 
ces derniers temps le sujet d’une multitude de plaisanteries 
assez mauvaises.’ 

Coming to modern philosophers,— Bacon of Verulam did not 
absolutely declare the syllogism incapable of furthering know- 
ledge, though he greatly preferred induction. He thought 
that it did not come up to the subtlety of nature, and that its 
proper place was among the more superficial disciplines (cf. 
§ 23). 

Des Cartes goes much further. In the proud consciousness 
of his own fresh mental power, he would throw overboard at 
once, as if it were merely ballast impeding the course of his own 


| Essai de Dial. rat., Annales de Math. vii. 227. 





344 § 101. Syllogism as a Form of Knowledge. 








mental discovery, syllogistic and with it all the Aristotelian and 
Scholastic Logic, the whole logical heritage of more than two 
thousand years, and would put in its place four simple rules 
which refer to one’s own subjective disposition in the investiga- 
tion of truth (ef. $ 24). And yet Des Cartes himself in his 
mathematico-physical investigations has made a most extensive, 
and, for the furtherance of the science, a most productive use 
of the despised syllogism. 

It is easily understood how the empiricism of Locke makes 
the syllogism of less value than external and internal ex- 
perience, induction, and common sense. 

Leibniz, on the other hand, recognises the logical rules, 
whose value he has learned to estimate in their application to 
mathematics, to be the criterion of truth (ef. § 27). He says 
more especially of syllogistic:? ‘The discovery of the syllo- 
gism is one of the most beautiful and greatest ever made by 
the human mind; it is a kind of universal mathematic whose 
importance is not sufficiently known, and when we know and 
are able to use it well, we may say that it has a kind of 
infallibility :—nothing can be more important than the art of 
formal argumentation according to true logic.’ This well- 
grounded judgment, however, when maintained in a one-sided 
way, occasioned the formalism of Wolff in the Leibnizian 
School, which frightened Kant into the belief that he must 
hedge in the syllogism within narrower bounds. He first cut 
off the second, third, and fourth figures as useless appendages 
(cf. $ 103), and then made the syllogism, thus supposedly 
purified from a false subtlety, no longer a means to extend 
knowledge, but only to make clear by analysis what we have 
already known. 

Fries, Herbart, and Beneke have adhered to Kant’s opinion. 

Hegel not only restored the syllogism to its former rights, 
but also explained it to be the necessary form of everything 
intelligible? He gave to it, when he identified it with the 
circular course of the dialectical adjustment of the moments of 


ı Essay, iv. 7. 2 Nouv. Ess. iv. 17, § 4. 
3 Log. ii. 119; Eneyel. § 181. 


Its Relation to the Real Reign of Law. 





the actual, a meaning so essentially changed, that the restora- 
tion did scarcely any good to the Aristotelian syllogism. Hegel 
has properly made it conspicuous that a distinction BT 
be drawn between the ‘ syllogism of totality’ as a “ syllogism 
of attention,’ and ‘the categorical syllogism’ as a ¢ syllogism 
of necessity.’ The major premise of the one has for its subject 
particular determinateness, the middle term has only empirical 
totality or the sum total of all concrete individual subjects, 
and therefore the conclusion, which should have that for its 
presupposition, itself presupposes it. The ‘ terms’ of the other 
‘according to their substantial content stand in identical re- 
ference to each other as existing in and for themselves,’ and, 
therefore, this inference does not, like the syllogism of reflection, 
presuppose its conclusion in its premises.! Trendelenburg has 
very acutely proved in his “ Logische Untersuchungen ’? that 
the Hegelian Logic itself is not free from inaccuracies and 
errors. 

Schletermacher asserts :* ‘ The syllogistic procedure is of no 
value for the real construction of judgments, for the substituted 
notions can only be higher and lower ;—nothing is expressed in 
the conclusion but the relation of two terms to each other, 
which have a common member, and are not without, but within 
each other. Advance in thinking, a new cognition cannot 
originate by the syllogism ; it is merely the reflection upon the 
way in which we have attained, or could attain, to a judgment, 
—the conclusion ;— No new insight is ever reached.’ But anew 
insight must always occur when two notions are combined in 
one judgment, which were previously separated from each 
other, and when united to any third, belonged to two different 
judgments. It did not escape Schleiermacher that an im- 
portant instance against his opinion is furnished by mathe- 
matical procedure, which evidently originates knowledge. 
But what he remarks against it is insufficient. He says, 
mathematical knowledge is not reached by means of the 
syllogistic form. All depends upon the discovery of the 


' Log. ii. 151, 162; Encycl. §§ 190, 191. 2 ji. 326-59. 
3 Dial. ὃ 327, p. 285; cf. p. 287 ff. 


€ 
= tra 


ot. geld BEG * 





Sates pe Sa πες τι 5 


Syllogism as a Form of Knowledge. 


construction. He who has it, has the proof, and only analyses 
the construction by means of the syllogism. ‘The true 
mathematicians do not depend upon the syllogism, but refer 
everything back to intuition.” These expressions upon the 
nature of mathematical knowledge are certainly untenable. 
The force of the proof does not lie in the construction, but 
in the application, which it renders possible, of propositions 
previously proved, and, in the last instance, of axioms and de- 
finitions, to the proposition to be proved, and this application 
is in its essence a syllogistie procedure.‘ The construction is 
only the way of learning, not the way of knowing, the scaffold- 
ing not the foundation. The proof rests (as Leibniz has 
rightly remarked) on the force of the logical form (ef. § 27). It 
is no mere illusion that the enlargement of mathematical know- 
ledge and its certainty is founded on the syllogism. This 
truth always lies at the basis of Schleiermacher’s remarks, 
that the cognition of syllogistic rules is not sufficient to 
find out the suitable syllogisms, but that there is needed a 
peculiar mathematical sense, a faculty of divining, and that 
this faculty, while it can, at a glance, penetrate through 
whole series of interwoven relations, need not prefer the broad 
form of completely developed syllogisms. There is in mathe- 
matics, as in common life, a fact or quick-sightedness, an 
ἀγχίνοια, which Aristotle? rightly defined to be εὐστοχία τις ἐν 
ἀσκέπτῳ χρόνῳ τοῦ μέσου, and on this gift depends the art of 
discovery. The essence of this ἀγχίνοια lies in the psychological 
relation, that the middle members of that series of thoughts, 
which lead to the result sought for, are thought in quick 
combination with complete objective truth, but with only : 
slight subjective strength of consciousness, while the last member 
of the series, or the result, is thought in the full strength of 
consciousness. The elevation of the individual members to 
complete clearness in consciousness is of little value for the 
discovery, but is of great importance to the certain scientific 
insight and for instruction. If then the peculiar nature of 


1 [Cf. Translator’s preface. | 2 Anal. Post. i. 34. 
3 Cf. Beneke’s excellent analyses of tact in his Lehrbuch der Psy- 


Its Relation to the Real Reign of Law. 347 





this quick-sightedness belongs not to logic but to psychology, it 
is evident that no objection can be raised from the side of the 
mathematical ἀγχίνοια against the foundation of mathematical 
certainty on syllogistic procedure. The mathematic vision 
passes over, in its flight, the same syllogisms, without being 
conscious of them individually as syllogisms, which mathe- 
matical analysis goes through in detail, and brings before con- 
sciousness. The logical essence of mathematical knowledge 
and the foundation of its certainty remain the same in both 
cases. 

Trendelenburg, who espouses the Aristotelian doctrine of 
the parallelism of the productive cause in the reality, and the 
middle notion in the logical syllogism, and advocates it very 
successfully,! when he approaches Schleiermacher’s opinion, 
expresses himself in the following way. Syllogism infers from 
the fact of the universal to the individual. The synthetic 
procedure, on the other hand, constructs the phenomena as a 
consequence from the general cause (reason, ground). The 
fact, on which the syllogism proceeds, may be the result of its 
internal foundation; but the universal fact comes solely znto 
consideration for the subsumption. The necessary reason 
clothes itself in the expression of a universal fact, and becomes 
in this form the middle notion of the syllogism. The power 
of the syllogism is formal only, not real, like the synthesis. 
Geometry gives to every advance the appearance of a syl- 
logistic subsumption, but the synthetic elements, which 116 in the 
construction and combination, work throughout by means of 
every syllogism and act creatively. The syllogistic procedure 
proceeds side by side with the synthetic, protecting it, and 
is its external representation. 'Thought in the synthetic pro- 
cedure is itself conscious of its accuracy, and in this way is 


for itself immediately certain. But if it wishes to represent to 


itself, or to others, what it has in its grasp, the connecting 


chologie, $ 158; Psychol. Skizzen, ii. 275 ff.; System der Logik, i. 
267 ff.; and Germar’s work, Die alte Streitfrage: Glauben oder 
Wissen ? Cf. also above, § 42. 

I Log. Unters. 2nd ed. ii. 354-58 ; 3rd ed. ii. 388-395. 





348 ὃ I01. Syllogism as ὦ Form of Knowledge. 


subordinating syllogisms serve to represent visibly the invisible 
course of thought. The individual vision of the synthesis is 
related to the syllogistic development, as measurement. with the 
eye is to the surveyor’s chain.’ The same objection which held 
good against Schleiermacher’s, holds good against this opinion. 
It is true that in mathematics only a very few propositions, 
and a few corollaries, can be proved by a simple syllogistic 
subsumption under others, and that for the most part in the 
constructions special ‘ synthetic elements’ are introduced ; and 
also that the discovery and combination of syllogisms leading 
to the end in view presuppose a mathematical ‘ vision, which 
is essentially different from the capacity to understand and 
appreciate the given syllogisms. But we cannot admit that 
the ‘synthetic’ combination is other than the combination of 
the judgments in syllogisms, and of the syllogisms in courses of 
inference; nor that the force of the proof and the certainty of 
the thoughts can lie in any other ‘ synthetic elements,’ than in 
the complex of syllogisms. For new knowledge can only be 
reached by deduction from the universal already known, and 
this deduction in its nature is necessarily syllogistic, for it can 
only happen by subsumption under the universal, however its 
syllogistic character may be concealed under the form of en- 
thymemes. The synthetic combination cannot be “ individual 
or ‘immediate’ in the sense that it does not subordinate the 
singular or particular in the case in hand to the general law, 
axiom, and previously proved theorems, and that it warrants 
to the thoughts in themselves an accuracy and certainty, as if 
by means of a hidden force. The truth is that the distinction 
of the ways of knowledge lies only in the measure of the 
strength of consciousness of the intervening members, in the 


I Log. Unters. 2nd ed. ii. 281; 3rd ed. ii. 314, where I am accused οἵ 


the misunderstanding of which I believe myself to be free, of think- 
ing that ‘the universal of facts’ must be, as facts, always derived from 
experience. I have only said, and argued from this, that, according to 
Trendelenburg, the fact only and not the reason is to be taken into 
consideration. For the other side, see Trendelenburg’s Log. Unters. 
Ind ed. ii. 354 ff.; 3rd ed. ii. 388 ff. 


Its Relation to the Real Reign of Law. 349 





permanence in consciousness of the individuals, or in their 
swift passage through it, in the completely stated or enthy- 
mematic form of the syllogisms. But above all it is not to be 
granted, that the syllogism and the complex of syllogisms does 
not produce new knowledge, but only serves to be the external 
representation for one’s own subjective certainty, and the 
means by which others may recognise what is already present, 
and, in another way, known certainly in itself and thought 
accurately without syllogisms ; nor is it to be allowed that for 
the syllogism as such the universal fact alone comes into con- 
sideration. For if the syllogism rests only on the universality 
of the fact, the objection of the Sceptics cannot be got over. 
The major premise cannot be established before the conclusion, 
and cannot serve as its foundation, and the Aristotelian doctrine 
of the middle notion is, at least for the syllogism as such, of no 
validity. If, on the other hand, the thought is essential for 
the syllogistic procedure that the ‘ universal of the facts’ must 
rest on the ‘ universal of the reason —and this is actually the 
case,—then the Aristotelian doctrine is valid. But then it is 
also false that, for the syllogism, only the universal fact comes 
into consideration, and that a ‘ synthetic’ procedure, other than 
that which completes itself in and by syllogisms, is required for 
the creative establishment of knowledge; and that the syllo- 
gism has only a ‘formal’ and didactic value. It must rather 
be recognised that syllogistic procedure is essentially ‘syn- 
thetic,’ and that all the other ‘synthetic elements’ to be in- 
cluded in the concatenation of syllogisms, are of use only for 
the discovery and application of suitable syllogisms. The 
‘ real’ power of the syllogism to produce knowledge shows 
itself not only in the mathematical, but in all the other fields 
of knowledge. Every intellectual apprehension of an in- 
dividual fact of history results necessarily from a universal law 
according to a syllogistic form of thought, although it is seldom 
expressed syllogistically. When, for example, in his ‘ History 
οἱ the Thirty Years’ War,’ Schiller explains the duration and 
violence of this religious contest, he points to a universal con- 


formability to law, according to which religious wars are 


oO 
oO 





350 § 102. The Simple Categorical Syllogism. 





carried on with the greatest pertinacity and bitterness, because 
every man may take the one side or the other with a personal 
self-determination, and not, as in national wars, in consequence 
of the merely natural determination of birth, and thus ina 
syllogistic form of thought subsumes the individual fact under 
this universal law. The view that the ‘power of the syl- 
logism is only formal and not real like the synthesis,’ is true 
only when limited to incomplete and unscientific syllogisms 
(whether of the first or of the other figures). It cannot be 
applied, if the Aristotelian doctrine of the middle term is true, 
to complete or specially scientific syllogisms, in which the ground 
of knowledge coincides with the ground. of reality. The dis- 
tinction, correct in itself, between the ‘ universal of the reason ’ 
and the “universal of the fact’ cannot serve as the basis for a 
distinction between ‘ synthesis’ and ‘ syllogism,’ but only for a 
distinction between two formations of the syllogism, and in refer- 
ence to the complete syllogism, between its ‘ real’ and “ formal ’ 
side. There are three essentially different opposites: 1. Reason 
and fact. 2. Tact and analysis. 3. Constructions and in- 
ferences. It is not necessary that the reason is apprehended 
only in the form of tact or vision, and is accompanied by con- 
structions, any more than that the opposed members, fact, 
analysis, and inference exist together; and accordingly it does 
not appear correct to comprehend the three first members 
under the common name of ‘ synthetic elements,’ nor to oppose 


reason and tact or vision to the syllogistic procedure, as if 


it were antagonistic to them. ‘* Synthetic : procedure is rather 
of svllogistie character, and the complete or truly scientific 
syllogism of “ synthetic ’ character. 


.$ 102. Tue SımpLE CATEGORICAL SYLLOGISM consists 


of three categorical judgments, of which two form the 
premises and the third the conclusion. They contain three 
chief notions ; that which is the subject in the ‘conclusion 


is the minor notion (terminus minor, ὅρος ἔσχατος, τὸ 
ἔλαττον sc. ἄκρον); that which is the predicate in the 


Its Three Terms. 351 








conclusion is the major notion (terminus major, ὅρος 
~ N ns ; 

πρῶτος, TO μεῖζον) ; the two together are the extreme 

notions (termini extremi, τὰ ἄκρα); and the common 

element mediating the inference is called the middle 

notion (terminus medius, ὅρος μέσος, τὸ μέσον). 

rt. . . . . . 

The premise which contains the major notion (ter- 
minus major), is the major premise (cf. $ 100), and that 
which contains the minor notion (terminus minor), the 
minor premise. 

This terminology was established by Aristotle. He defines:! 
ὅρον δὲ καλῶ eis ὃν διαλύεται ἡ πρότασις. οἷον TO TE κατηγορού- 

\ \ a lal Ν 
μένον καὶ τὸ καθ᾽ οὗ κατηγορεῖται."Σ καλῶ δὲ μέσον μὲν ὃ καὶ 
αὐτὸ ἐν ἄλλῳ καὶ ἄλλο ἐν τούτῳ ἐστὶν, ὃ καὶ τῇ θέσει γίνεται 
¥ Ν > > 3 x 
μέσον " ἄκρα δὲ TO αὐτό τε ἐν ἄλλῳ ὃν Kal ἐν ᾧ ἄλλο ἐστίν ---- 
7 Ν “ Ν » > N ° 5 
λέγω δὲ μεῖζον μὲν ἄκρον ἐν ᾧ τὸ μέσον ἐστὶν, ἔλαττον δὲ TO 
e \ \ / ” 
ὑπὸ TO μέσον Ov. In the same passage and elsewhere, Aristotle 
x ey eo . - 
uses also the names: ὁ ἔσχατος ὅρος (terminus minor), and 
ὁ πρῶτος (terminus major). He formed this terminology 
having regard to that form of the syllogism in which the rela- 
tion of the spheres of the three notions agrees with the verbal 
meaning of the names: μεῖζον or πρῶτον (the wider or higher), 
μέσον (the middle), and ἔλαττον or ἔσχατον (the narrower or 
lower notion). He then transfers it? to the other forms, where 
the relation of sphere is otherwise, and correspondingly modi- 
fies its meaning. If the definitions are given as equally 
applicable to all cases (which is a scientific demand that 
cannot be refused), the relation of spheres cannot come into 
consideration. The middle term is in some cases in the first 
form or figure of the syllogism only the mean according to 
extent ; it must generally be defined as that which mediates 
(the inference). The other two terms cannot be distinguished 
from each other in an equally universally valid way, if their 
NP . = 4 > 
relation as subject and predicate in the conclusion be not 
attended to. Their relation of spheres (although a specially 


I Anal, Pri, i. 1, 2 Ibid. i, 4. 3 Ibid. i. 5, 6. 





352 § 103. Three Chief Classes or Four Divisions 





fixed one in the fundamental form of the first syllogistic 
figure) is one which in general is completely indefinite. It 
might appear then as if the reference to the conclusion were a 
fallacious ὕστερον πρότερον, and as if every attempt at a general 
distinction of the major and minor terms must necessarily 
miscarry.' Syllogistic would then lose much of its scientific 
definiteness, and a thoroughgoing distinction of moods would 
be impossible. But in fact, there is no fallacy whatever in 
that reference to the conclusion. It is only the universal 
form of the conclusion (S P, ie. either A B, or B A, if A 
and B are the extremes) which is by hypothesis brought 
under consideration. There is no reference either to the dis- 
tinct formation (Sa P or Se P, &c.) which the conclusion 
may take, or to the question whether a conclusion of that 
form can at all exist;—all that is to be found out by further 
investigation. The, general form (either A Bor BA) can 
without harm be presupposed, and the designation of the 
different notions in the premises founded upon it. 


§ 103. Simple Categorical Syllogisms divide into 
three chief classes, which are called SYLLOGISTIC FIGURES 
(figurae, σχήματα); and the first of these divides into 
tuo subdivisions, which are also designated Syllogistic 
Figures. The division into three chief classes rests on 
the relation of the middle term in the premises as 
subject or predicate to the other two notions, without 
reference to the distinction of major and minor term, 
and consequently without reference to the form of the 
conclusion, on which the general distinction of these 
two terms from each other is founded. The middle 
notion is either subject in the one premise and predicate 


1 Trendelenburg, Log. Unters. 2nd ed. ii. 309 ff., finds this fallacy 
in the distinction ; and Drobisch, Log. 3rd ed. p. 92, asserts, that the 
distinction, whether a or B is the subject of the conclusion, is an 


arbitrary anticipation. 


of the Simple Categorical Syllogism. 363 





in the other, or predicate in both premises or subject in 
both. In the first case the first chief class or First 
Figure in the more comprehensive sense results. The 
second case gives the Second, and the third case the 
Third chief class or Figure of the Categorical Syllogism. 
The subdivision rests on an included reference to the 
distinction between the major term (that notion which 
is predicate in the conclusion) and the minor term 
(that notion which is subject in the conclusion). This 
subdivision establishes two sections in the first chief 
class: in the first, the middle term is subject to the 
major term and predicate to the minor ; in the second, 
it is predicate to the major and subject to the minor. 
The first section of the first chief class is the First 
Figure in the narrower sense. The second section of 
the first chief class is the so-called Fourth or Galen’s 
Figure. In the second and third chief classes, the dis- 
tinction of major and minor term gives no analogous 
subdivision, for in both the relations of the major term 
and of the minor term to the middle are the same. 
Both in the second figure take the place of subject in 
the two premises, and in the third figure that of pre- 
dicate; and their exchange, therefore, does. not alter 
the general relation. 


According to what is said above three or four Syllogistic 
Figures may be spoken of with equal correctness, as the name 
figure is used in the more comprehensive or more limited sense. 
We may say that there are three because there are three chief 
classes. We may say that there are four, because the first 
class has two sections; each of the others coincides with a 
Section, and so there are in all four sections. The uncritical 
confusion of the two divisions is fallacious. The first method 

AA 





ὁ 103. Three Chief Classes or Four Divisions 


354 of the Simple Categorical Syllogism. 55 


of division (into three Figures with two divisions in the first) 
has always a greater formal accuracy, just as the division of 
bodies according to their condition as aggregates into— 








ον the second method of division S, P, and M again find 
. . “Ὁ 

PP ge But since the expression figure is now understood 

n ὺ : ; 

in the narrower sense, four Figures result, the first of which 


I. Flowing bodies, (a) fluid, (4) liquid ; 
II. Solid bodies.—is to be preferred in formal reference 
to the division into (1) fluid, (2) liquid, and (3) 
solid bodies ; 
but it is a pedantic rigorism which attaches too much weight 
to this (cf. § 64). On the other side, the second method 


of division (into four Figures) has its value in didactic and 
It is simpler, and more thoroughly se- 
licated methods of inference, 
he second division 


scientific reference. 
parates the artificial and comp 
which belong to the Fourth Figure (or to t 
of the First Figure in the wider sense), from the simple and 
natural forms of the First Figure in the narrower sense. 
Schematic representation may make both methods of division 
sensibly evident. If we call the middle notion (terminus 
Medius) M, and the other two notions, without previously re- 
garding their distinction as major and minor term, A and B, 
then, according to the ‚first method of division, the Schema of 
the three chief classes is the following :— 
I. II. III. 
M A A M M A 
B M BM M B 


The form of the conclusion (B A or A B) rem 
consideration; but if we distinguish the major and minor terms, 
and call the minor, because it becomes the subject in the con- 
clusion (Subiectum conclusionis), $, and the major, because it is 


1 the conclusion (Praedicatum conclusionis), P, the 
in 


ains out of 


predicate ἢ 
first chief class or the First Figure in the wider sense, 


which the word is used in the ‚first method of division, divides 
into its two divisions, while the Second and Third remain 
undivided, according to the following Schema :— 
| oe Ἰ, 1 ie 11. III. 
M P PM PM M P 
S M M > S M MS 
A: a Fs 


Ss P S pP 


corresponds to the first division of the First Ficure in the 
wider sense, the second to the Second Figure, the thiva to the 
τ ὃς igure, and the fourth to the second division of the 
irst Figure in the wid ‘di i 
ead ul er sense, according to the following 
Ir, IIV. IV’, 
PM M P m 
MS MS 


Ss P S | jee 


It is self-evident that the conclusion in all cases must take the 
form S P, for the meaning of S is that it denotes that one 
which becomes the subject of the conclusion, and the meani x 
of P is that it denotes the predicate of the conclusion. It tar 
not be necessary even to allude to this if it were πὰ sider 3 
some logical works the question, which shows a com ake 
understanding, has been asked, Why should one so a 
alway? come to the conclusion S P, and why is not the ee 
P S also admissible ? ' It is certain that if the terms outsid 
of M are immediately, without any further distinction call i 
A and B, the general inference to B A is as ET a z 
AB ; but if the conclusion has the one form, then B is se a 
(Subiectum conclusionis) and A the P (Praedicatum co 1 
sionis) : if it has the other form, then A is the S, and Β περ P. 
The relation of the major term to the minor in the iii 
is a definite one; in the premises it is indefinite. a 
their position in the conclusion must serve as the foundati ᾿ 
of their distinction, and therefore their designation in tl | = 
clusion should not change. Ἴ iy 
The succession of premises is in all cases without influenc 
on the determination of the Figure. It is useful to place is 





ıB 
" oe who has otherwise stated Syllogistic very well says 
0g. p. 2% é . . ll, says 
ἊΣ ie 26), ‘ Another fancy of the Aristotelians was to draw the 
sion S P for all Figures; but this is not at all necessary.’ 
AAQ 





356 § 103. Three Chief C lasses or Four Divisions 





major premise first, and it is practically convenient to keep to 
the one definite succession of premises in the logical explana- 
tion of syllogistic relations in order to guard .. oa 
sights, and prevent errors. But this does not mean that ἣν 
procedure in the syllogism is linked to this one method of “a 
cession. The other is quite as admissible, ın which the above 
Schemata take the following form :— 


I, 1orT. I, 2 or IV’. II or Il’. 
ΝΜ MS S M 
M P PM PM 


; ΞΡ 5. 


. . . . . J 2 in 
This succession of premises 1s easier and more eee ΜΝ 
1 ' iti subject before 
the First Figure, at least (the position of the ubj en 
” . . . ῷ 
the predicate is presupposed in single propositions), and occul 
i j it 1 - 1m 
oftener in actual inferences. But it 1s not necessary, 1 
logical explanation, to depart from the mode of gg a 
. . . » Φ . n 
in use since Aristotle’s time. “It is rather advisa & Ἑ 
: τὰ 
didactic reference, to keep to it, although too > weig 
i i 1 ᾿ 6 expres- 
should not be given to it, because it only concerns tl x] + 
sion. The essential thing is this, that the succession In 16 
expression of the premises is not to be nn one 6, 
1 es not esta- 
and that the mere change of external position : : er 
i ‘ sion. 
blish a change of the form or figure of the conclusio 


example, the syllogism— 


III or III.’ 
MS 
MP 


Ss P 





AM 
MB 


A B 


i i : it is said that the 
is called a syllogism of the Fourth Figure ; or ıt 1s said that 
‘inverse order,’! or that there are 
premises here stand in the ‘ inverse order, : 
1 ren 5 ary 
in all? eight forms (one fundamental form, and seven = ᾿ 
‘ioures ἢ ination of the 
forms, or seven ‘ Figures’), by means of a combi =. 
above Schemata I’, II’, III’, IV’, and of those following the 
, . 
from: I, 1, or I’, &e. 
1 Prantl, Geschichte der Logik, i. 587. 
2 As the Kantian Krug thinks. 


of the Simple Categorical Syllogism. 357 


J 





Aristotle usually preferred to place the predicate before the 
subject in those judgments which form the syllogism. For 
example, a syllogism of the First Figure, according to him, 
is stated in the following way :— 


> \ \ \ ~ 
εἰ TO A κατὰ παντὸς Tov B, 
\ \ nw 
καὶ τὸ Β κατὰ παντὸς τοῦ Γ, 


» \ \ \ aA A 
ἀνάγκη τὸ A κατὰ παντὸς τοῦ I’ κατηγορεῖσθαι. 


In this way the terms from the most universal (the πρότερον 
φύσει) to the most special (the ὕστερον dice) follow each other 
successively, and their arrangement is conformable to nature 
in this reference. 

In this way Aristotle uses the ὑπάρχειν : e.g. εἰ τὸ M τῷ μὲν 
N παντὶ τῷ δὲ ἘΞ μηδενὶ, οὐδὲ τὸ N τῷ & οὐδενὶ ὑπάρξει (on the 
other hand the expression, ἐνεῖναι, e.g. τὸν ἔσχατον ὅρον ἐν ὅλῳ 
εἶναι τῷ μέσῳ καὶ τὸν μέσον ἐν ὅλῳ τῷ πρώτῳ ἢ εἶναι ἢ μὴ εἶναι, 
has the meaning: to be contained in the extent of the wider 
or higher notion as a subordinate notion, and in the judgment 
to form the subject to that). 

The following is an old Scholastic example of the Four 
Figures:! 1. Every virtue is praiseworthy ; Eloquence is a 
virtue: Eloquence is praiseworthy. 2. No vice is praise- 
worthy ; Eloquence is praiseworthy: It is not a vice. 3. 
Every virtue is praiseworthy; every virtue is useful: Some- 
thing useful is praiseworthy. 4. Every virtue is praiseworthy ; 
everything praiseworthy is useful: Something. useful is a 
virtue. 

Aristotle divides syllogisms into three Figures (σχήματα), 
the first of. which he explains at length in the Prior Analytics 
l. ον iv., the second, ib. c. v., and the third, ib. c. vi. He calls 
the syllogism of the First Figure perfect (συλλογισμὸς τέλειος). 
because in it the result follows from the premises immediately 
(without the aid of sentences coming in between, which accord- 
ing to his view is required in the other F igures). The syl- 


' According to Lambert and Rosenkranz, Log. ii. 153. 
2 Anal. Pri. i. 1. 





358 § 103. Three Chief Classes or Four Divisions 








logisms of the two other Figures are incomplete (συλλογισμοὶ 
ἀτελεῖ). The thought also influences him in this terminology, 
that a universal affirmative conclusion can result, and the 
ground of knowledge coincide with the real cause, in the First 
Figure only. 

The relation of this Aristotelian division to the division into 
Four Figures which was common in the latter part of the Middle 
Ages, although some very valuable researches have already 
been direeted towards this point, requires strieter investigation. 
The common account is, that the three Aristotelian Figures 
coincide with the first three of the later division (the above I’, 
Il’, ILI’), and that the fourth (IV’) was added by Cl. Galenus. 
On the other hand, Trendelenburg' has sought to show that the 
Aristotelian division is as complete as the later, but rests on a 
different—and really better—principle. ‘ Aristotle distinguishes 
three Figures, according as the middle term in the series of sub- 
ordinate notions takes the middle place (First Figure), or forms 
the highest (Second Figure), or lowest notion ( Third Figure). 
When we look at the subordination of the three notions neces- 
sary to a syllogism, three figures result. When four figures 
came to be enunciated, another ground of division was followed: 
the possibility of the different positions which the middle notion 
may have in the two premises. Aristotle saw the internal 
relation of the three terms present in the inference; the ex- 
ternal relation which was afterwards looked to consisted in the 
position of the middie term as subject or predicate in the two 
premises. Aristotle did not take the succession of premises 
into consideration; but one succession only is allowed by 
modern logicians, according to which the notion, that is the 
subject in the conclusion, 1s always referred to the minor pre- 
mise. This order is an arbitrary arrangement, and the inverse 
of the natural relations ; for the conclusion following from the 
premises can in no case influence its grounds (the premises ): 
‘Qui terminorum naturam spectant, eos tria figurarum genera, 
qui externam enunciationum formam, eos quatuor constituere 


1 Log. Unters. 2nd ed. ii. 308 ff.; 3rd ed. ii. 341 ff.; cf. Elem. Log. 
Arist. § 28, and Explanations of the Elements, same paragraph. 


of the Simple Categorical Syllogism. 359 





necesse est. Quare Galenus non addidit, ut vulgo putant 
quartam tribus prioribus, sed tres Aristotelis in giästuor wa 
convertit; nituntur enim plane alio dividendi fundamento. In 
order to settle this question of debate, we must, with direct 
reference to Aristotle, distinguish between the principle of his 
division and its application. 

So far as the principle is concerned, one thing is undoubted 
that the relation of a successive subordination RR the eas 
notions requisite to the syllogism exists in the First Figure 
only; and even there not everywhere, for it does not unit in 
negative and particular judgments. In the Second Figure, as 
Trendelenburg himself remarks,' and mostly in the Third this 
relation ‘is more an assertion of an andlogy than strictly a for 
the negation breaks the connection of the subordination.’ It fol- 
lows from this as certainly, that Aristotle, 7f he attempted the 
division of syllogisms into figures upon the internal relations of 
the subordination of terms, on a relation which actually exists in 
the first of these figures only (and not even in this throughout) 
made a decided blunder, and that if the Aristotelian Sylloeinie 
is free from this incorrectness, it ought to be recotmnined 
to be free from it. The relation between the terms which 
actually exists, is the judgment relation, that the middle 
notion is either subject in the one premise and predicate in the 
other, or predicate in both, or subject in both. If Aristotle 
selected, as the ground of division, this relation, which is 
also an internal and essential, apart from the distinction be- 
tween the two other notions, his procedure would be justifi- 
able, and his three principal σχήματα would coincide with 
our three chief classes. T'rendelenburg? founds his opinion: 
( 2 On the Aristotelian Definitions of the single figures ;? 
(2) On the Aristotelian reduction of the Second ang Third 
Figures to the First; and in the first edition of his work,‘ 
he also (3) makes the explanation of Aristotle® equivalent ἰο: 


: Log. Unters. 2nd ed. ii. 314; 3rd ed. ii. 347. 

Ibid. 2nd ed. ii. 310; 3rd ed. ii. 343. 3 Anal. Pri. i. c. iv.-vi. 
u: 238, in a note which is left out in the later editions. 

® Anal. Pri. i. δ. v. 





360 § 103. Three Chief Classes or Four Divisions 











the middle notion in the Second Figure is ‘ the highest’ (πρῶ- 


ἢ θέσει). 

ae to ᾿ first point, it is correct that the Aristotelian defini- 
tion of the First Figure rests on the principle of successive 
subordination which is true in its fundamental mood. This 
definition is:! ὅταν ὅροι τρεῖς οὕτως ἔχωσι πρὸς ἀλλήλου» ὥστε 
τὸν ἔσχατον ἐν ὅλῳ εἶναι τῷ μέσῳ, καὶ τὸν μέσον ἐν ὅλῳ τῷ 
πρώτῳ ἢ εἶναι ἢ μὴ εἶναι, ἀνώγκη τῶν ἄκρων εἶναι συλλογισμὸν 
τέλειον, and to it are annexed the definitions of the μέσον and 
the ἄκρα given in the former paragraph. The definition of ἣν 
Second Figure, however (or rather of the second possible way 
of combining the premises, the question. whether a valid _- 
ence results or not being previously abstracted), is as nie : 
ὅταν δὲ τὸ αὐτὸ τῷ μὲν παντὶ τῷ δὲ μηδενὶ ὑπάρχῃ» ἢ ἑκατέρῳ παντὶ 
ἢ μηδενὶ, τὸ μὲν σχῆμα τὸ τοιοῦτον καλῶ δεύτερον. This definition 
evidently does not presuppose the principle of rn 
but only the judgment relation that the middle term ıs A 
cate in both premises; for Aristotle adds the a: μέσον δὲ 
ἐν αὐτῷ λέγω τὸ κατηγορούμενον ἀμφοῖν, ἄκρα δὲ καθ᾽ ὧν λέγεται 
τοῦτο. The same is true of the definition of the aes 
Figure (or rather of the third way of combination), won 
is as follows:? ἐὰν δὲ τῷ αὐτῷ TO μὲν παντὶ τὸ δὲ μηδενὶ 
ὑπάρχῃ, ἢ ἄμφω παντὶ ἢ μηδενὶ, τὸ μὴν ne iti vr καλὰ 
τρίτον. Aristotle adds: μέσον δ᾽ ἐν αὐτῷ λέγω καθ᾽ οὗ ee 
τὰ κατηγορούμενα, ἄκρα δὲ τὰ κατηγορούμενα, 80 that here the 
judgment relations are specially taken into consideration. = 
Secondly, as to the Reduction of the individual ways 0 
inference in the Second and Third Figures to that of the First, 
it serves the purpose of proving the validity of the deduced 
‘nference. It does not follow from this kind of ee 
that according to the view of Aristotle the Second and Thin 
Figures must rest on the principle of successive subordination, 
which is partially true in the First. | 
At the most, the third point seems to favour the view that 
Aristotle looks upon the relation of the terms ın all three 


foures as a relation of successive subordination. He says ol 
oO 


1 Anal. Pri. i. 4. 2 C. v. 3 C. vi. 


of the Simple Categorical Syllogism. 361 


0 





the middle notion of the First Figure:! ὃ καὶ τῇ θέσει γίνεται 
μέσον" of the second: τέθεται δὲ τὸ μέσον ἔξω μὲν τῶν ἄτρων, 
πρῶτον δὲ τῇ θέσει ; andofthe third:* τίθεται δὲ τὸ μέσον ἔξω 
μὲν τῶν ἄκρων, ἔσχατον δὲ τῇ θέσει. He also says‘ the μεῖζον 
ἄκρον (terminus maior) is τὸ πρὸς τῷ μέσῳ κείμενον in the Second 
Figure, but the ἔλαττον (terminus minor) τὸ ποῤῥωτέρω τοῦ 
μέσου, and’ the converse relation exists in the Third Figure. 
All these assertions conform very well to the view that a suc- 
cessive subordination of the terms exists in all three figures, 
and if it were shown on other grounds that Aristotle entertains 
this view, that they are to be explained by it. It is another 
question, however, whether they can be explained only on 
this view, and whether they justify an inference back to it. 
For this view, as has been shown, is a wrong one, and is 
to be attributed to Aristotle in his syllogistic only, if his words 
admit of no other natural explanation, and only in propor- 
tion as the words necessitate it. These expressions, how- 
ever, always admit of a more favourable meaning (which 
Waitz has followed in his commentary on c. v. p. 26, b. 37). 
The expression θέσις may be understood of the position or 
arrangement of the terms in the premises, which rests on the 
relation of subject or predicate, and of the position hereby 
conditioned in the shorter Aristotelian Schema. The funda- 
mental form of the First Figure is the following :— 


\ \ \ - 
τὸ A κατὰ παντὸς τοῦ B, 


\ \ \ a 
τὸ Β κατὰ παντὸς τοῦ I’, 





\ A 
τὸ A κατὰ παντὸς tov I. 


The θέσις, positio, collocatio, of the middle notion B is the 
mean betwixt A and I’, and Aristotle therefore places the terms 
of the First Figure shortly together in the following order :— 


A BT, 


or, as we (with Trendelenburg) ® might write it, if we denote 
the middle notion by the capital letter :— 


I Anal. Pri. i. c. iv. .Vv (0: vi 
NW. 6 Erläut. p. 52. 


~ 5 ' é “Ὁ fe νυ ἐδ. 
u oy Ἂς ᾽ν ἐδ τ εν 
Sw ll teal ea an ee u u = 





362 $ 103. Three Chief Classes or Four Divisions 


J 





In this figure the relation of its extent may coincide with the 
relation of the terms in the premises, and with the external 
position resting on this relation ; but this does not prevent the 
most immediate meaning of θέσις from denoting the judgment 
relation, and this meaning from being the only one in the 
remaining figures. The fundamental form of the Second 
Figure is, according to the Aristotelian way of representation :— 


\ \ Ἁ m 

τὸ M κατὰ μηδενὸς tov N, 
\ \ \ m 

τὸ Μ κατὰ παντὸς τοῦ 5, 








\ A 
τὸ N κατὰ μηδενὸς τοῦ 


The middle term here, or the part mediating the inference, Μ, 
is the first in position, πρῶτον τῇ θέσει, because as the predicate 
it precedes the other notion in both premises. The shorter 


Schema 15 :— 


ΜΝΞ, 


or, as above, to distinguish the middle term from the other 


two :— 
M ν &. 

If the assertion of Aristotle about the middle term in this 
figure is easily explained from its predicative relation in the 
premises, without the false presupposition of a successive 
subordination of the terms, the wider question always includes 
and accounts for the fact that Aristotle separates the major 
term, τὸ μείζον, from the minor, τὸ ἔλαττον. He says (see 
above) the major is here the nearer to the middle notion, the 
minor the further from this. This coincides with the position 


in the Schema :— 


M v &. 


But on what does this rest, and on what, more especially, does 
the placing v before ἕ rest? We may easily go back a step further 
to the previous more detailed Schema, in which likewise the N 
follows immediately after the first M, because that one of the 
two premises which contains the N should be placed before the 
other by Aristotle. But how does this happen? What is 
the reason for this preference of one premise to the other? 


of the Simple Categorical Syllogism. 363 


J 








It appears as if we should be here obliged to return to the 
opinion, that Aristotle had entertained that false presupposi- 
tion of a relation of logical subordination existing heen 

and ἕξ, and all the more because the terminology μεῖζον ia 
ἔλαττον brought over from the First Figure Second this view 
And in truth this much must be granted, that Aristotle ii 
this terminology, has allowed himself to be guided be i 
analogy which does not always hold good, but ih was 
excusable in the circumstance because he recognised (with 
complete correctness) the First Figure to be the form most 
important scientifically, and looked on the others (in this going 
too far) as dependent forms of less value. He made ὼς 
v however parallel to the major of the First Figure, and the 
& parallel to the minor, and gave the precedence to the pre- 
mise which contains the v, and so we must seek for the cause 
but not necessarily in an erroneous opinion upon the internal 
relation of these terms. Aristotle may have come to a deter- 
mination (more unconsciously) by the same reflection upon the 
form of the conclusion which the later logicians expressly 
explain to be the reason for the distinction ‘at the major and 
minor term, as well as of the major and minor premise 
although he does not introduce this consideration into his 
division of the figures of the syllogism. (The passage in the 
Anal. Pri. i. 23, where Aristotle proceeds from the conclusion 

and defines according to its form that of the premises, ai 
favours this.) All those expressions of Aristotle may be 
explained in a natural way without recourse to the hypothesis 
of an error. The Third Figure is to be explained in the 
same way. The Schema of its fundamental forms is, according 
to the Aristotelian representation, the following :— i 


\ \ - 
τὸ II κατὰ παντὸς τοῦ &, 
\ \ m 
τὸ P κατὰ παντὸς τοῦ 2, 





τὸ II κατὰ twos τοῦ P. 
The shorter Schema is :— 
se = 
or (according to the above manner of representation) :— 
wp & 














| VISTONnS 
364 § 103. Three Chief Classes or Four Divisi 





The notion mediating the inference, the 2, ἔσχατον τῇ θέσει, 
is here the subject both times, and is, accordingly, in ~~ 
shorter Schema placed last. In this figure, when both seem 
are affirmative and universal, the middle notion is reiki y 
subordinate to the other two notions. This relation, howev μ᾽ 
does not exist in other modes of inference in this figure, ἜΣ 
tigated by Aristotle no less carefully, so at 2 we eet 
also explain the position, θέσις, οὖ Σ from its m: er 
it happens to be subject-) relation. Besides, a definite rela : n 
of subordination does not necessarily exist between m and p 
in the case where both premises are affirmative and universal, 
much less in all inferences of the Third Figure; and when 
Aristotle calls that term in this figure the minor, which is 
nearer the middle notion, and that term the major, which 
stands further from the middle notion, this position and the 
connected terminology are to be explained in the same way as 
in the Third Figure. . 

Trendelenburg’s three arguments do not prove that Ari- 
stotle has endeavoured to establish the division of syllogisms 


δ imaginar relation of | 
into three Figures on an imaginary threefold re 


subordination between the three terms. Aristotle expressly 
enunciates the principle of his division :! ἐὰν μὲν οὖν κατηγορῇ 
καὶ κατηγορῆται τὸ μέσον, ἢ αὐτὸ μὲν κατηγορῇ; ὅλο ὃ = 
ἀπαρνῆται, τὸ πρῶτον ἔσται — δον δὲ “a hd be Ρῃ ῳ 
ἀπαρνῆται ἀπό τινος, τὸ μέσον. ἐὰν ὃ ἄλλα ἐκείνου πρό τὸ : 
ἢ τὸ μὲν ἀπαρνῆται τὸ δὲ κατηγορῆται, τὸ ἔσχατον"---τῇ = 
μέσου θέσει γνωριοῦμεν TO σχῆμα. According to . 
the position, θέσις, of the middle notion in the premises, es 
the figure; but this position rests In its turn on the re ation 
of the middle notion as subject or predicate in the premises. In 
this division the distinction of major and minor term does not 
come into consideration. The unambiguous principle of divi- 
sion here laid down by Aristotle is not a secondary point A 
view, but is fully identical with that principle, which, Br 
ing to the above explanation, lies at the basis of the —— 
of the three figures (or rather of the three syzygies condition 


1 Anal. Pri. i. c. xxxll. 


of the Simple Categorical Syllogism. 365 





ing the figures) in chapters iv., v., and vi., and to which Ari- 
stotle himself refers in c. xxxii. in the words: οὕτω yap εἶχεν 
ἐν ἑκάστῳ σχήματι TO μέσον. (Cf. Anal. Pri. i. 23, p. 41 a, 
14: ἢ yap τὸ A τοῦ T καὶ τὸ T τοῦ B κατηγορήσαντας ἢ τὸ IT 
κατ᾽ ἀμφοῖν ἢ ἄμφω κατὰ τοῦ Τ', ταῦτα δ᾽ ἐστὶ τὰ εἰρημένα 
σχῆματα.) So far as we keep to what is general and principal, 
that either firstly the middle notion is predicate in the one 
premise (κατηγορῇ), and at the same time subject in the other 
(κατηγορῆται unusually for τοῦτο ἦ καθ᾽ οὗ κατηγορεῖται, prae- 
dicato exornetur, sustains predication),! or secondly is predicate 
in both, or thirdly subject in both,—this Aristotelian distinc- 
tion of the different judgment relations of the middle term in 
the premises establishes a complete division of all simple cate- 
gorical syllogisms into three figures, and in this respect we can 
assert as the result of our investigation up to this point, that the 
Aristotelian principle of division of syllogisms agrees with the 
principle of our above-mentioned division into three ch vef classes, 

Another question arises,—Is the application of this prin- 
ciple in Aristotle complete, or does it break down in the second 
division of First Figure? Itis a fact that Aristotle does not 
divide his First Figure into two sections, and that he does 
not formally explain the particular way (or moods) of infer- 
ence which belong to its second section or to the later so-called 
Fourth Figure, at least not in the same manner as he does 
the other ways of inference; and he has not placed them on 
a level with these others. They were first added (cf. below) 
by other logicians to the Aristotelian Moods. Ik is also 
evident that in the nearer determination of the First Figure,? 
according to which the subordinate notion falls within the 
extent of the middle notion, and the middle notion either falls 
within or is completely excluded from it, the extent of the super- 
ordinate notion only belongs to the first section of the First 
Figure, or to the First Figure in the more limited sense (I’). 
It is evident also that the definition in c. xxxll., so far as it has to 


' Cf. Trendelenburg, Elem. Log. Ar. at § 28, and Waitz on the 


passage, 


2 Anal. Pr. i. c. iv. 











366 ὃ 103. Three Chief Classes or Four Divisions 





do with the First Figure in the more comprehensive sense, 
does not expressly take into consideration the distinction of 
the major and minor terms,—that according to its fundamental 
thought it would comprehend all the moods of both sections, 
—that it may be applied in its single determinations not 
merely to those of the section, but also to some moods of the 
second (viz. Bamalip, Calemes, Dimatis, of which more below) 
__and that in consequence of the limiting determination, accord- 
ing to which the premise which contains the middle notion as 
predicate can only be affirmative, it cannot apply to the rest 
of the ways of inference in the second division (viz. to Fesapo 
and Fresison). 

Aristotle has, however, given in two passages indications 
which only need to be followed out, in order to find the Moods 
belonging to the second section of the First Figure. He says! 
that if a special syllogism cannot be constructed, a conclusion 
may be found in a certain position of the premises, in which 
the minor term (τὸ ἔλαττον) is the predicate, and the major (τὸ 
μεῖζον) the subject. This case occurs, if the one judgment 
affirms universally or particularly, and the other denies uni- 
versally. When (according to the way of combination in the 
First Figure) A belongs to every or Some B, and the B to 
no I, it results necessarily, when the premises are converted, 
that some A are not I. (Conversion brings it to the Syl- 
logism: Ferio of the First Figure: some A is B; no B is I’; 
Some Ais ποῦ Γ. In the application of the expressions: μεῖζον 
and ἔλαττον, Aristotle has, in this case, been led by analogy 
only to use the designations which he uses in the syllogisms 
recognised by him to be completely valid.) The moods here 
signified (as the old exegetes have remarked) are identical with 
those which were afterwards considered to be the last two of the 
five moods of the second division of the First Figure (1, 2) or of 
the Fourth Figure (IV’), viz., Fesapo and Fresison. Aristotle 
remarks in the same place, that the same happens in the other 
figures also; for a conclusion is always reached ‘by Con- 
version (ἀντιστροφή) of the premises. But the moods, accord- 


1 Anal. Pri. i. ce. vil. 


of the Simple Categorical Syllogism. 367 
ing to which inferences can be made in the other Forms 
not new ones, but coincide with distinct kinds or iors: ὦ 
inference already explained by Aristotle. (These are Cesar 
Camestres, and Festino of the Second Figure, which b Done 
version of both premises pass over into Ferison of the Thir 7 
and F elapton and Ferison of the Third, which pass over a 
Festino of the Second.) Aristotle says further,! that all those 
syllogisms whose conclusion universally ἜΝ universal] 
denies, or particularly affirms, yield a second result, if the ae 
clusion be converted, while a particular negative PR 
according to the universal rule of conversion, admits of no sin 
version. Aristotle does not distinguish the cases in which the 
inference reached by the conversion of the conclusion coincides 
with one of the already explained moods or methods of infer- 
ence (such as Cesare, which passes over into Camestres by this 
conversion, and Camestres into Cesare, Disamis into Datisi, wi 
versa; while an inference in Darapti only passes over into EEE 
inference of the same mood) from those cases where a new result 
is attained which is not attained by any other way of inference.? 





I Anal. Pri. ii. ο. i. 
| . Waitz has not appreciated this essential distinction when he says :* 
Apulei librum nullius fere pretii esse facile inde coniicitur quod 
ubi de prima figura disputat, Theophrastum imitatur in corals 
propositionibus, in tertia vero eum reprehendit, quod opinatus sit duos 
modos nasci ex conversione conclusionis.’ In the same way. Pr; Ä 
calls the procedure of Apuleius ‘simple.’ ἡμῖν cae! 
ναὶ , ple. On the contrary, the true 
view lies at the foundation of the assertion of Apuleius, that the syl- 
logism with a converted conclusion in the First arse We 
another division, and therefore to another mood; nd in the Third 
Figure, Darapti is only another example of inference in the same 
mood. The mood is determined by its essential attributes, which enter 
= its definition. The relation, in which the conclusion of the syl- 
ee τ - = of another, does not belong to 
ae pre 16 conversion of the conclusion 
ΟἹ ἃ syllogısm In one case (viz. when a change of essential attributes is 
connected with it) leading to a new Mood, and in another case not. | 





* Org. i. 386. T Gesch. der Log. i. 370. 





=— 


——- 


ee ee 


ER eee = 


ae 


a 


eons 2 


ταν 
Se 





— — us ne 
uct tts 


SE SE 


ei 


TEE ei Be 


tec 


—— 


as 


x 


ae nn πῷ 


363 § 103. Three Chief Classes or Four Divisions 





If, however, these last cases were singled out, they are those 
(as the old commentators remarked) which afterwards became 
the first three of the five Moods of the second division of the 
First Figure (I, 2) or of the Fourth Figure (IV’), viz. Bamalip, 
Calemes, and Dimatis, and which may be produced from the 
three corresponding moods of the First Figure, Barbara, Cela- 
rent and Darii, by Conversion of the conclusion, although they 
need not necessarily originate in this way. Cf. below. 

The disciples of Aristotle, Theophrastus and Eudemus, have 
added the five ways of inference, which result as a new acquisi- 
tion from those Aristotelian indications, to those modes of in- 
ference recognised to be fully valid and strictly explained 
by Aristotle himself. They number them from the jifth to 
the ninth mood of the First Figure, in the order which re- 
mained in use afterwards (viz., 5. Bamalip, 6. Calemes, 7. Di- 
matis, 8. Fesapo, 9. Fresison). Alexander of Aphrodisias, 
the Commentator,’ and Boéthius attest this! The former 
says: αὐτὸς μὲν (ὁ ᾿ΑριστοτέληΞ5) τούτους τοὺς ἐγκειμένου5 συλ- 
λογισμοὺς δ᾽ ἔδειξε προηγουμένως ἐν τῷ πρώτῳ σχήματι γινομέ- 
νους, Θεόφραστος δὲ προστίθησιν ἄλλους πέντε τοῖς τέσσαρσι 
τούτοις οὐκέτι τελείους οὐδ᾽ ἀναποδείκτους (i.e. not as the first 
four moods, evident without proof) ὄντας, ὧν μνημονεύει καὶ 
᾿Αριστοτέλη----τῶν μὲν τριῶν τῶν κατ᾽ ἀντιστροφὴν τῶν συμπερα- 
σμάτων γινομένων τοῦ τεπρώτου ἀναποδείκτου καὶ τοῦ δευτέρου καὶ 
τοῦ τρίτου ἐν τῷ δευτέρῳ κατὰ τὰς ἀρχάς .---τῶν δὲ καταλειπομένων 
δύο ἐν τούτοις οἷς λέγει ὅτι-- ἐν ταῖς ἀσυλλογίστοις (συξυγίαι5) 
ταῖς ἐχούσαις τὸ ἀποφατικὸν καθόλου καὶ οὔσαις ἀνομοιοσχήμοσι 
(i.e. where the premises are of different quality) συνάγεταί 
τι ἀπὸ τοῦ ἐλάττονος ὅρου πρὸς τὸν μείζονα" αὗται δέ εἰσιν 
ἐν πρώτῳ σχήματι δύο συμπλοκαὶ ἥ τε ἐκ καθόλου καταφατικῆς 
τῆς μείζονος (SC. προτάσεωΞ) καὶ καθόλου ἀποφατικῆς τῆς ἐλάτ- 
τονος, καὶ ἡ ἐξ ἐπὶ μέρους καταφατικῆς τῆς μείζονος καὶ καθόλου 
ἀποφατικῆς τῆς ἐλάττονος "---ὧν τὸν μὲν ὄγδοον, τὸν δὲ ἔννατον 
Θεόφραστος λέγει. Boéthius® says, habet enim prima figura 


1 Alex. Ad Anal. Pri. f. 27 8. 2 Anal. Pr. ii. c.i. 
3 Ibid. i. c. vil. 4 Cf. ibid. 42 2-43 a. 
5 De Syll. Categ. Oper. ed. Basil. 1546, p. 594. 


of the Simple Categorical Syllogism. 369 


2 








sub se Aristotele auctore modos quatuor, sed Theophrastus 
vel Eudemus super hos quatuor quinque alios modos addunt 
Aristotele dante principium in secundo priorum Analyticorum 
volumine ;' hoc autem, quod nuper diximus (viz. the con- 
version of the conclusion in Darii, Celarent and Barbara) 
in secundo priorum Analyticorum libro ab Aristotele mon- 
stratur, quod scilicet Theophrastus et Eudemus principium 
capientes ad alios in prima figura syllogismos adiiciendos 
animum adiecere, qui sunt eiusmodi, qui κατὰ ἀνάκλασιν νο- 
cantur, Le. per refractionem quandam conversionemque pro- 
positionis (according to which Boéthius numbers the moods 
V—IX).? 

It is these five Moods which were afterwards separated from 
the First Figure, and collected together under the Fourth or 
Galen’s Figure. Galen’s own writings, so far as we have 
them, do not show that he was the author of this mode of re- 
presentation. All logicians of note in the whole of the later 
antiquity down to Boéthius have followed the method of Theo- 
phrastus, and reckoned these five as moods of the First Ficure. 
There is no mention in the whole of ancient literature, with 
the exception of two single notices discovered lately (of which 
anon), that there is any other mode of representation. All 
accounts of the much-talked of discovery by Galen, those two 
notices excepted, go back to the testimony of the Arabian 
philosopher Averroés, which in the old Latin translation is as 
follows :>—Sin autem dicamus: A est in c, quoniam ¢ est in B 
et Bim A, res erit, quam nemo naturaliter faciet ;—et ex hoc 
planum, quod figura quarta, de qua meminit Galenus, non est 
syllogismus, super quem cadat naturaliter cogitatio. — Ad- 
ducitur deinceps terminus medius, qui praedicetur de prae- 
dicato quaesıtı et subliciatur subiecto quaesiti, secundum quod 
erıstimavit Galenus hanc figuram quartam esse, secundum quod 


' Boéth. De Syll. Categ. Oper. ed. Basil. 1546, p. 595. 
ar . ἃ. ὦ . e 
| Cf. Philop. Ad Anal. Pri. f. xxi.B: οἱ καλούμενοι avravar\@perot. 
Cf. Prantl, Gesch. der Log. i. 365 ff., 700. 
° Averr. Prior. Resol. i. 8, f. 63 B, ed. Venet. 1553. 


BB 








370 § 103. Three Chief Classes or Four Divisions 





refertur ad quaesitum. Of those two lately discovered pas- 
sages, the modern Greek Minoides Minas has found the one 
in an unedited anonymous commentary on the Aristotelian 
Analytic, and has published it in his edition of the Pseudo- 
Galen’s Eicaywy? διαλεκτική The words are: 5. -Θεύφραστος 
δὲ καὶ Εὔδημος καί τινας ἑτέρας συζυγίας (synonymous with 
τρόπους) Tapa τὰς ἐκτεθείσας τῷ ᾿Αριστοτέλει προστεθείκασι τῷ 
πρώτῳ σχήματι ---ἂς καὶ τέταρτον ἀποτελεῖν σχῆμα τῶν νεωτέρων 
ὠήθησάν τινες ὡς πρὸς πατέρα τὴν δόξαν τὸν Ταληνὸν 
ἀναφέροντες. Minas has given nothing more exact about 
the Commentary, and so the time from which the extracted 
notice dates remains very uncertain.° 

Prantl gives us the other passage in the second volume of 
his History of Logic in the West,‘ from a work of Johannes 
Italus (a later contemporary of Psellus), the Διάφορα Ζητήματα:" 
τὰ δὲ σχήματα τῶν συλλογισμῶν ταῦτα" ὁ Γαληνὸς δὲ καὶ τέ- 
ταρτον ἐπὶ τούτοις ἔφασκεν εἶναι, ἐναντίως πρὸς τὸν Σταγειρίτην 
φερόμενος. Itis certain that the discoverer of this figure did not 


add it as one ‘lately found out’ to those earlier known, but 


only presented what was already known in his time in a new 
form. He divided the nine moods of the First Figure, in the 
wider sense of Aristotle and Theophrastus, into two figures, 
the First in the stricter sense and the now so-called Fourth 
Figure. Galen in his endeavours to represent Logic as far as 
possible in a mathematical way :°_dxorov0joat τῷ χαρακτῆρι 
τῶν γραμμικῶν dmodsi£eoav—might be led to this separate re- 
presentation of the Fourth Figure. 

The view which Trendelenburg asserts in a passage quoted 
above, that the division of Figures into four rests on the 
external form and position of the propositions, and presupposes « 
settled course of succession in the premises, is untenable. This 
principle would rather have led toa division into eight, a position 
to which Krug only has fallen (cf. above, p. 356). The division 


’ 


2 Προθεωρ. pag. ve. 


1 Paris, 1844. 
3 Cf. Prantl, Gesch. der Log. 1. 532 f. 

4 Gesch. der Logik im Abendlande, ii. 295. 
6 De Prop. Libr. x. xix. 40 Η. 


5 Fol. 330. 


of the Simple Categorical Syllogism. 371 


2 





into four rather involves complete freedom of external posit; 
and succession, and the principle of the division is Eetitgnichel 
from that of Aristotle and Theophrastus only by direct] 
taking into consideration the universal distinction between the 
major and minor term, and the distinction between major and 
minor premise, which rests on the former. It neither de pends 
on wee conditions an absolutely fixed external succession Th 
Scholastic term ‘ metathesis praemissarum ’ sienifies chief ἂς 
change of internal relation, by which the ns ee 
the major premise (in the sense established by the definition) 
becomes the minor premise, and the former minor ur 
a ae the major, the external en a the 
"0 ION 1 i 
pP a Si connected with this only as a useful formula 
The Scholasticism of the Middle Ages, which appropriated 
the syllogistie procedure, perhaps not with entire ee 
going comprehension, but all the more with the most unbound d 
faith, allowed itself to be robbed of no Fieure and of no M a 
The division of Theophrastus remains in poe co-ordinate vith 
the so-called Galen’s division. Many of the Humanists pa 
Modern Philosophers, on the other hand, in the first heat of th 
struggle against a form of culture which had outlived it if 
threw overboard without distinction the whole a 
imaginary ) rubbish of Scholastic subtlety, amongst which 
many included Syllogistic. Others again, especially in ae 
times, took a middle course; but, because for the er t 
they lacked the deeper understanding, they were led t qe 
external via media rather than to a true mean. Thes Hogi a 
was not abandoned because it was seen to be indis ie, 
but in order not to fall under the scorn of the < less 
and in order to make things more comfortable, its wines wate 
— as it were, and a certain respect only was ‘paid to 
oe ee: dry, redundant treatment gradually 
oe = 5 : roug t syllogistic completely into contempt. 
wie: = = whom strictness of syllogistic form was a 
us heart as strong as that of the most zealous 


BB2 











372 § 103. Three Chief Classes or Four Divisions 





Scholastic, and who himself eminently deserved the title of a 
ς demonstrator optimus,’ which he gave to Joachim J ungius, the 
author of the Logica Hamburgensis, an earlier logician, believed 
that the tendency of the time had to be so far considered that 
in his lesser Logic, written in German, he treated of the First 
Figure only, and in his ampler Latin works the first three 
figures, leaving unmentioned the moods of Theophrastus, 
Wolff teaches! that the syllogisms of the First Figure are the 
most natural, because they contain direct application of the 
Dictum de omni et nullo. They are sufficient to establish all 
possible conclusions. The First Figure is therefore figura 
perfecta. The other two are figurae imperfectae, because they 
contain only indirect applications of that axiom, and cannot 
establish all kinds of conclusions, especially not the universally 
affirmative, which is the most important for science. Their 
moods do not all lead to a knowledge of the reason why the 
predicate belongs to the subject, “non continere rationem, unde 
intelligitur, cur praedicatum conveniat subiecto.” To this, 


which agrees in all essentials with Aristotle’s doctrine, Wolff, 


going further, adds,? ‘ syllogismi secundae 
figurae sunt syllogismi eryptiei primae ;—apparet adeo, non 
opus esse, ut peculiares pro iis figurae constituantur. 

In opposition to the preference which Wolff gives to the First 
Figure, becauseitalone follows from the Dictum de omni et nullo, 
Lambert, in his Neues Organon,‘ places the four figures on an 
equality. He founds the Second Figure on a Dictum de Diverso: 
Things which are different do not belong to each other τ᾽ the 
Third on a Dictum de Exemplo: ‘ When one finds things A 
which are B, then there are A which are B ;’ the Fourth on ἃ 


Dictum de Reciproco: ‘ If no M is B, no B is this or that M; ıl 


c is or is not this or that B, there are B which are or are not C. 
With the help of diagrams (which, limited to straight lines and 
points, are greatly inferior in didactic value to the circle sym- 
bols) he seeks to show that the other figures are as capable 


2 Ibid. § 393. 
4 Leipzig, 1764. 


1 Log. § 378 sqq. 
3 Ibid. §§ 385, 397. 


syllogismi tertiae 


of 


of the Simple C, ategorical Syllogism. 373 


2 





immediate derivation from the nature of the axioms as tl 
First. The First Figure is naturally and unconsciousl aaa 
to prove qualities, the Second to prove differences the Third 
to prove examples and conceptions, and the F ourth to prov 
reciprocities. as 
Kant, who did not much lik rlloeisti 
in some degree aa u een 
| € . In his treatise 
‘proving the false subtlety of the four syllogistie figures’ (1762 
he enunciated the axiom that pure rational BE are a 
in the First Figure only, and mized inferences (ratiocinia ἣ ἜΡΟΝ 
or impura) in the other three,! and that division into acd 
generally, in so far as they contain simple pure inferences wale. 
out a medley of auxiliary judgments, is therefore false aid im- 
possible. It is not, as Kant in his treatise thinks, ‘ indisputable 
that all the figures, with the exception of the First, determine 
their consequences by a circumlocution and a medley of 
inferences coming in between.’ The conclusion in the other 
figures may be directly found (as will afterwards be shown) 
without the need of reduction to the First. Even if that reduc- 
tion was needed for the purpose of proving their correctness 
(as Kant, in agreement with older logicians, believed), the 
would as little lose their position as new and inde idea 
syllogistic figures, as would a mathematical axiom which must 
found itself on an axiom proved earlier, neoosserily sink to the 
place of a dependent corollary. The syllogisms of the last 
three figures would remain “ simple’ syllogione even if their 
proof had to be established by means of an waiilieny judgment 
for the definition which makes the simple syllogism to be i 
inference from three terms only in two given judgments would 
be no less applicable. Hence they must be co-ordinate with 
syllogisms of the First Figure, as the other kinds of simple 
syllogisms (or, if one would question the correctness of this 
terminology, as hinds of syllogisms from three terms). The 
‘Aristotelian recognition of the less scientific value of these 
syllogisms is not incompatible with this co-ordination. The 
charge which Kant adds ? is quite peculiar : If it happened that 


1 ν nr 
Cf. Log. § 65. 2 On the False Subtlety, §c., p. 35. 





of the Simple Categorical Syllogism. 375 


374 § 103. Three Chief Classes or Four Divisions 








chosen according to one’s fancy: ‘ Those natural philosophers 
who affirm an existence between water and air to be the prin- 
ciple, account for the existence of individual essences by 
rarefaction and condensation ;’ ‘ Anaximander on his principle 
accounts for the existence of individuals not by renelaction 


a number of inferences, which were blended together under the 
principal judgments, became so mixed up with them that when 
some were expressed others were unexpressed, it would take a 
great deal of art to judge of their agreement with the rules of 
inference, and one would be able to contrive not only more 














figures, but still more puzzling inferences, fit to break one’s head. 
But the aim of Logic is not to confuse, but to solve, to advance 
something not in a concealed way but openly. Hence these 
four kinds of inference should be simple, not hybrid nor mixed 
up with secondary inferences, or else they cannot be allowed to 
appear in a logical statement as forms of the most significant 
representation of an ‘inference of reason.’ _ 

This assertion rests on a complete misconception of the 
nature of the case. The charge resembles that which might 
be brought against Astronomy, if one were to blame it because 
it imagines such complicated cases, and enunciates such diffi- 
cult calculations, that they rack the brains of learners instead 
of remaining stationary at the simplest and easiest statements. 
Since the heavenly bodies are not polite enough to wheel in 


circles, nor yet to avoid perturbations in order to spare the - 


astronomer’s headaches, his calculations must be adjusted to 
all the cases present. In the same way the problem of the 
logical doctrine of inference is to consider exhaustively the 
different cases which occur in actual thinking. When two 
judgments of definite form, having one notion common to 
both, are presented in the. thoughts with which logical laws 
have to do, they are not always actually so placed as iS 
most eonvenient for the purpose of forming an inference; 
they may have all different kinds of relations to each other. 
The different cases are not contrived by logicians, nor are 
they examples for the illustration of the notion of an infer- 
ence of reason unhappily chosen and very confused; they 
represent the various possibilities which, although not all 
equally frequent, are yet realised in actual thought. For 
example, the historical critic lights upon the following testi- 
monies of Aristotle. They come to him in a certain form 
which he cannot alter as he might in an artificial example 


and condensation, but by separation.’ These propositions do 
not belong to the scheme of the First Figure, and yet the 

lead naturally to a definite and valuable Ba N It We 
to positive thinking to determine in every single case while 
there is a valid inference or not, and it Bi to Tas to 
lay down completely in an exhaustive division the different 
relations possible, and to enunciate their universal laws 
Drobisch justly remarks in this reference! that it ER 
belongs to the strictly scientific demands to develope completel) 
the possible forms of inference, because the critical atthe 
into the value of the single modes of inference can only depend 
upon an exhaustive survey. 

| When several modern logicians, like Hegel and Herbart, and 

in spite of the assertion quoted above, Drobisch also τῆνος 
the modes of inference of the Fourth Figure (or the wee υ of 
Theophrastus), or, like Trendelenburg, reject the Third Figure 
also or certain of its moods, we may recognise this truth 

that the scientific value of the debated modes of inference Ἢ 
less in comparison with the others, but we may not for this 
reason proceed to reject them altogether. The ambiguity and 
danger of going wrong, which Trendelenburg says sdtanhen to 
them, although it does exist in most of them, and might exist 
in Darii and Ferio of the First Figure, vanishes when we 
strictly and accurately settle what belongs to the notion of the 
particular judgment. 

We cannot approve of Hegel’s plan of making the Second 
and Third Figures change places. The exchange is not 
warranted by any internal necessity, and FOREN use 
and wont in these things only creates confusion. 

| Hamilton’s New Analytic of Logical forms makes Figure 
only an unessential circumstance. For if the predicate be 


! Log. 2nd ed. pref. xiii. 











376 § 103. The Simple Categorical Syllogism, ete. 








rigidly quantified, then the copula marking the relation of 
subject and predicate may be dispensed with, and the algebra- 
ical sign of equality (=) may be used instead. When this is 
done, we may have terms which are not related as subject and 
predicate, and inferences which do not belong to any Figure. 
Hence syllogisms are either: (1) Unfigured, where the terms 
are both subject or both predicate, or either indifferently ; 
where there is no order of terms, for they may be enounced 
first or second indifferently ; and where all difference of major 
and minor term or proposition is’ abolished. For example, 
One who practically adopts the utilitarian theory of Ethics in 
solving difficulties in morals, and one who acknowledges this 
theory, are equivalent; Kant and one who practically adopts 
the utilitarian theory of Ethics in solving difficulties in morals 
are equivalent: therefore Kant and one who acknowledges 
this theory are equivalent (Mill’s argument).—(2) Figured 
where two forms of syllogism result by different orders of 
terms:—(a) First Figure, where two forms of conclusion are 
possible. For here the middle term is subject of the one 


extreme and predicate of the other, and there is a determinate - | 


major extreme and premise, and a determinate minor extreme 
and premise: consequently, also, one proximate indirect, and 
one remote or indirect conclusion,—the latter by the con- 
version of the former.—(b) Second and Third Figures are the 
reverse of the first. They have no major and minor extreme 
and premise, both extremes being subjects or predicates of the 
middle: consequently, in the inference, as either extreme 
may be indifferently subject or predicate of the other, there are 
two indifferent conclusions, that is, conclusions neither of which 
is more direct or indirect than the other. Hamilton abolishes 
the Fourth Figure as a hybrid and as useless.’ 

De Morgan adopts the four figures because the external 
combination of three terms in two propositions (the premises) 
gives four combinations. He seems to say that the Fourth 
Figure is the more natural.’ | 


[! Lect. on Log. ii. 404. 2 Formal Logic, p. 130.] 


$ 104. Combination of the Premises, etc. 377 


§ 104. Each of the two premises of the categorical 
syllogism in reference to quantity and quality may ke 
of four different forms ;—of the form: 





a, i.e. All A are B; 


or of the form: 


e, 1.e. No A is B; 


or of the form: 


i, 1.e. At least a part of A is B 


(At least one or some A are B); 
or of the form: 


O, i.e. At least a part of A is not B 
(At least one or some a are not B). 


Hence in each of the two divisions of the first class and 
ἴῃ each of the other classes there are sixteen. in all 
sixty-four, forms of combining the premises. If the jirst 
letters symbolise the form (quantity and quality) of the 
major premise (which contains the major term, ie. that 
notion which forms the predicate in the conclusion 
whose existence we prove), and the second letters the 
form of the minor premise (which contains the minor 
term or subject of the conclusion), the sixteen combina- 
tions may be represented in the following Schema :— 

aa ea ia 04 

ae ee ie oe 

ai ei ii oi 

a0 eo io 00 


These forms of combination lead only partially to valid 


Sy 1 1 > 
yllogisms. The single modes of inference or kinds of 





378 ὃ 104. Combination of the Premises, ete. 





syllogistic figure which rest on the different forms of 
combination of the premises in reference to quantity 
and quality, are called moods (modi, τρόποι τῶν σχη- 
μάτων). 

The repeated reference to the meanings of the symbols: 
a, 6, i, O, and of the expressions major premise and minor pre- 


mise, is justified by the fact that embarrassing mistakes so 
frequently arise about them. 

The procedure by combination borrowed from Mathematics 
(which was probably first brought into use by the Peripatetic 
Aristo of Alexandria)! has been very much condemned. It 
has been called mechanical and irrational. Prantl? calls it a 
< Game of Mosaic’ which ‘fundamentally disavows the Arı- 
stotelian middle notion, and compares it to what he calls the 
‘combination-game of the childish imbecile Stoics,’ &c.; but 
-incorrectly. It is true that the chief matter of interest 
for syllogistic does not lie in the single figures and moods, but 
in the universal principles of syllogistic. But the principle 


itself expands into the system. If it be justly considered that - 


something valuable has been done when natural science, by 
empirical collection of the discoverable species to any one 
genus, has reached complete cognition, how much higher must 
the gain be when we succeed in reducing the forms possible to 
a universal principle, and in proving with mathematical accu- 
racy the completeness of the enumeration ? Syllogistic is able 
to do this in its province; and procedure by mathematical 
combination is an indispensable instrument. The nature of 
the thing demands this, and it is quite in conformity with 
reason. The charge of ‘mechanism’ and its external appear- 
ance need not alarm us. He who will have nothing to do 
with ‘mechanism,’ where it properly exists, is in danger of 
giving himself up to mere abstractions, as Hegel does in the 
physical, and more especially in the astronomical parts of his 
natural philosophy. Is then ‘the mechanical’ a ‚necessary 
and unavoidable presupposition in all the departments of 


1 Of. Prantl, Gesch. der Logik, i. 557, 590. 2 Ibid. 


from attri ik i 
ibute to attribute, or from predicate to predicate * ;—or 


] 


g . 
᾿ § 105. Comparison of Spheres, ete. 379 
organic and spiritual life? The expression of Lotze’s wh; 

is the fundamental ee 
| ntal conception of his ‘ Mikrokosmos’! gives 
the true answer: ‘ T’he mechanism is nowhere the essence of the 


thing ; but the essence never presents itself in any other form of 
Jinıte existence than that which is supplied by the 





mechanism.’ 


105. or a ΟἹ inati 
§ The testing whether a given combination le 


eee ads 
to valid inferences, and the proof of the validity or 


in- 


validity st der 

| it) ‚ must depend upon the comparison of the spheres 
u . . i Ἵ 
within which, according to the premises, 


κόρ | | the notions 
nder consideration find application. These spheres 


suitable for that comparison are made apparent to the 
; , 

‘iis by geometrical figures (especially by circles) 
2 .Ψ r= . . ε 
whose reciprocal relations agree with the relations of 


the spheres of the notions to each other in all relations 
essential for demonstration. 


It h 
t has νῶν already remarked above? that this kind of com- 
ATISO 
P ἐς n o N men In no way presupposes a thorough-going 
ἢ a Ὁ ω . . 
= substantive predicate notions. The possibility remains 
ol p 
I ἜΝ the whole procedure (as Aristotle does),? under the 
oN 1 1 
sr of view of a subsumption of lower notions, under similar 
r ones,— 
a »—or (as Kant does, who explains the axiom: “ nota 
a . . .Ψ δ 4 
e est nota rel Ipsius ; repugnans notae repugnat rei ipsi,”4 
to be the principle of all ical i Υ a 
principle of all categorical inferences of the re 2 
of regarding it from the poi Bu 
g g it trom the point of view of an advance in thought 
oO 


9 


astly (as Trendelenburg does),” of uniting both points of view 
' Mikrok. i, 487; 2nd ed. i. 451. 2 § 71 
° Anal. Pri. i. c. iv. sqq. | 


4 - . 
Which Aristotle had already enunciated and with a more accurate 


apprehension. Cf. Categ. c. iii. 


5 ἢ); : Er 
Die falsche Spitzfindigkeit d. vier Syllog. Fig. erwiesen, $ 2; 


Log. $ 63. 


6 . i 
[Which is almost Mr. Mill’s opinion. See Log. 1. 201.] 
Log. Unters. 2nd ed. ii. 315 ff.; 3rd ed. ii. 348 ff. 





380 § 105. Comparison of Spheres 








and recognising in the conclusion a reference of the content to 
extent, and of the extent to the content.’ In the different 
single examples, where the syllogistic form is the same, some- 
times the one, sometimes the other, and sometimes the third 
view, will be the more suitable, according as the predicate 
denotes (a) in both the genus of the subject, or (b) in both an 
action or property, or (c) in the major premise an action or 
property, and in the minor the genus. The three following 
syllogisms are all categorical of the First Figure (and the 
mood Barbara), and yet they fall naturally successively under 
the view of subsumption, of inherence, and of the (subsuming) 
subjection of the particular under the (inhering) predicate or 
law of the universal:—(1) Every planet is a heavenly body; 
the earth is a planet; Therefore it is a heavenly body.—(2) 
All right-angled triangles have such a relation of their sides 
that the square of the hypothenuse is equal to the sum of the 
squares of the other two sides; All triangles which may be 
inscribed in a semicircle, so that one side is the diameter, are 
right-angled ; Hence they have this relation of sides discovered 
by Pythagoras. (Triangles in order to be inscribed in a 
semicircle are not to be subsumed as a species under the genus 
right-angled triangles, but are identical with them; the in- 
ference proceeds from property to property.)—(3) All similar 
triangles have the same relation of sides: those triangles, into 
which the right-angled triangle is divided by the perpendicular 
from the vertex of the right angle to the hypothenuse, are 
similar to each other (and also to the whole, which has been 
divided); therefore they have the same relation of sides. 
Aristotle makes the relation of spheres the foundation for 
syllogisms of the First Figure, reduces those of the other 
figures to the First, and proves the invalidity of the forms of 
combination not suitable for inference, by producing examples, 
in which a conclusion is yielded and supposed to be valid, 


[! As Hamilton substantially does, with the difference that 'he does 
not unite the two opinions and make them the basis of one syllogistic 
procedure, but separates it into two orders of syllogisms, those in 


Extension and those in Comprehension. ] 


as a Criterion of Capability for I. nference, 381 


o 








while its material falsehood is recognised in some other wav 
This demonstration is convincing in so far as the hy τ ὃ oe 
the validity is overthrown by the falsehood of i of age : 
sequences. It lies under a twofold difficulty we a) 
that for the sake of the proof, a datum wie than τῶν : ; 
manded must be added; (2) the ground of the RR of 
the invalidity does not correspond to its real ground a 
Later logicians base the rules for the rajoctiiie oe certai 
fundamental axioms (viz. that the middle notion may ries 
particular in both premises, and must not stand in : mer ly 
negative relation to the other terms, and that no saat is τς. 
taken in the conclusion in a more universal extent than Ἢ μὰ 
corresponding premises), which result from a comparison of 
spheres, and this comparison of spheres is applied by hs of 
the definitions in $ 71. But the immediate οὐδ δῥο νι: of 
spheres in each of the individual rules is the more convenient 
. | Hamilton, by a thorough-going application of the quantifice- 
tion of the predicate, gets rid of the ordinary rules of sylloeisn 
and shows ὃν validity of several moods which are ae 
ne ai syllogism can be formally wrong in which : (1) 
premises are not negative; and (2) The quantifications of 
the middle term, whether as subject or predicate, taken togetl 
— the quantity of the term taken in iis whole cee 
de se ge RR no syllogism can be bad. 
g y mutual subordination, and may 
be of any figure. The result is an increase of the losical 
moods, For the doctrine of the quantification of the un 
gives eight instead of four propositional forms to beein with: 
and when these eight forms are combined according en 
et and quality, they give thirty-six valid ad (twel un 
afirmative a renty-four LV 
2 vr. ᾿ ee negatıve); and these thirty-six 
The history of the comparison of spheres by means of geome- 
‘rical schemata has already been explained at § 85, Ρ. 234 f. 


ar ae ΠΕ eee 

: ὸ Cf. Hamilton’s Lect. on Log. ii. 853-57, 457-60, 475, 476; and 
Pr « ni ? a . > . 
rot. Baynes’ New Analytic of Logical Forms, p. 74. ] 





382 $ 106. Er Mere Negativis Nihil sequitur. 





§ 106. On application of this means of testing, we 
find that in all the figures of the categorical syllogism 
no inference can be drawn from merely negative premises. 
‘Ex mere negativis nihil sequitur.’ For— 

(a) If both premises are universally negative, then the 
middle notion (M), which (according to $$ 100 and 
102) must enter once into each of the two premises as 
subject or predicate, must be thought to be completeiy 
separated from the other two premises (A and B); and 
the relation of these to each other remains wholly un- 
determined. The premises admit of the three possible 
cases: (1) that the sphere of the one of the two ex- 
tremes is quite separate from that of the other; (2) that 
the one lies partly within and partly without that of the 
other; and (3) that the one falls quite within that 
of the other. This is represented by the following 


Schema: 


The Forms EE, OF, EO, Ὁ Ο cut of. 383 





Hence there is no definite relation between A and B 
which can be expressed in a valid conclusion. | 

(b) If the one premise be universally and the other 
particularly denied, then M must be thought to be quite 
separated from one of the two terms and (at least) partly 
separated from the other. But the partial validity of 
the negation, according to the logical notion of the par- 
tieular judgment ($$ 70 and 71), never excludes the 
possibility of the universal negation, and. does not 
necessarily include the validity of the particular affirma- 
tion. Hence the whole indeterminateness, which exists 
between two universally negative premises, remains, 
and is still more increased by the additional possibility 
of other relations. Consequently a definite result is 
still less given. 

(c) If both premises are particularly negative, then, 
for the same reason, the .indefiniteness is increased. 
Hence no definite conclusion can result. 


If the particular negative judgment meant: only some are 
not, but others are, it would then yield a definite conclusion, 
provided the other premise was universally negative. It would 
then not be the consequence of the double negation, however, 
but of the particular affirmation implicitly thought along with it. 





384 ὃ 106. Ex Mere Negativis Nihil sequitur, etc. 





The axiom: ἐν ἅπαντι (συλλογισμῷ) δεῖ κατηγορικόν τινα τῶν 
ὅρων εἶναι was enunciated by Aristotle.' Now there is of course 
a case in which a valid conclusion may be obtained from two 
negative premises. If the premises are given: What is not M 
is not P; and: S is not M—the inference follows: S is not P. 
But this inference does not fall under our above-given defini- 
tion of the simple syllogism (§ 100), as a syllogism from three 
terms; for there are here four terms: S, P, M, and not-M 
(that, which is not M). If this is reduced to a simple syl- 
logism, the minor premise must (by means of an immediate 
inference per aequipollentiam, cf. $ 96) take the form: 5 isa 
not-M. But then it is according to quality an affirmative 
judgment (§ 69), and the rule, that from merely negative pre- 
mises nothing can follow in a simple syllogism, may remain 
unchanged. This reduction is not an artificial mean, con- 
trived in order to violently reconcile an actual exception to a 
rule falsely considered to be universally valid. We only 
arrive naturally at the conclusion, when we think the minor 
premise in the form: S falls under the notion of those beings 


which are not M. 


ὃ 107. Ex Mere Particularibus Nihil sequitur, etc. 385 





In the Middle Ages Duns Scotus combated the universal 
validity of the rule: Ex mere negativis nihil sequit a 
ground of that case. ; a i 

Wolff enunciates the axiom:! si terminus medius fu ‘it 
negativus, propositio minor infinita est (negandi particula = 
refertur ad copulam, sed ad praedicatum),? and a: 
equidem non ignoro, esse qui sibi persuadeant, steriles ae 
nugas, quae de propositionibus infinitis aliisque aequi sled: 
bus in doctrina syllogistica dicuntur, eum in finem ae: 
ut per praecipitantiam statutae regulae salventur; but justl 
repels this view because his doctrine necessarily follows fr : 
the notions of the terms. The later logicians have su fici lly 
passed over this question. 5 ding 

According to the rule established in the foregoing 
oO 


graphs, the premises in the following el 


forms of combination 


cannot lead to valid inferences :-— 


ee ΟΘ 
eo 00 


ee eee 


.— 


sought to solve the difficulty by this very reduction. Boéthius only from which an inference can be obtained 
says :? ‘ Sed fuerunt, qui hoc quum ex multis aliis, tum ex twelve: — mee 
aliquo Platonis syllogismo colligerent ;—in quodam enim dia- | aa 
logo Plato huiusmodi interrogat syllogismum : sensus, inquit, 
non contingit rationem substantiae; quod non contingit ra- | 

tionem substantiae, ipsius veritatis notionem non contingit ; | ai ei “<4 
sensus igitur veritatis notionem non contingit. Videtur enim | 20 

ex omnibus negativis fecisse syllogismum, quod fieri non potest, | 
atque ideo aiunt, infinitum verbum, quod est: non-contingit, 
pro participio infinito posuisse, id est: non-contingens est „—et 
id quidem Alexander Aphrodisieus arbitratur ceterique com- 
plures.’ It is not improbable that the doctrine of qualitative 
Aequipollence between two judgments owes its origin to the 
explanation of the syllogistic case. 


‚to the following 


ea oa 
ae 


¢ . 

a 107. In all figures of the simple categorical syllo- 
ΟἹ ῷ 44, 7 ᾿ Ὶ 
sism, no valid inference results if both premises are 


ar o ᾿ 6 5 . © . 
: ticular, ‘Ex mere particularibus nihil sequitur.’ 
On 


ı Anal. Pri. i. 24. 


2 Ad Arist. de Interpr. p. 403; Prantl, Gesch. der Log. i. $ 559. | Log. § 377 * Ibi 
! | : id. § 208. 3 Ibid. § 377 
| cc 








386 ὃ 107. Ex Mere Particularibus N thil sequitur. 








(a) If both are particularly affirmative, then only an 
indefinite part of the sphere of the middle notion is 
united with an indefinite part of the spheres of either of 
the two remaining terms. If the middle term is the 
subject in any one of the premises, or in both, the 
assertion holds good, according to the particular form 
of the judgment for an indefinite part only of the sphere 
of the middle notion. If it is predicate, the same in- 
definiteness arises from a more universal reason, because 
in every affirmative judgment it remains unexpressed 
whether the sphere of the predicate wholly or only 
partially coincides with the sphere of the subject (cf. 
§ 71). Hence it remains indefinite whether the same 
part of the middle notion or a different part is united 
with the two other terms in the two premises, and it 


is also uncertain in what relation they stand to each | 


other. Hence no conclusion is obtained. | 

(b) If the one premise is particularly affirmative and 
the other particularly negative, it is also indefinite with 
what part of the sphere of the middle notion the one 
extreme is particularly connected, and from what part 
of this sphere (if the middle notion is the subject in 
the other premise) the other extreme is separated, or 
whether the middle notion (if it makes the predicate in 
the other premise), while it is quite separated from ἃ 
part of the sphere of the other extreme, is also, wholly, 
in part, or not at all, separated from the other part οἱ 
this sphere. If it is also uncertain, whether the two 
extremes have any definite relation to one and the same 
part of the middle notion or not, the relation in which 
they stand to each other is the more uncertain. Hence, 
again, no definite conclusion can be reached. 


But 


The Forms of Combination II, OL I O cut of. 387 








(c) If both premises are particularly negative, then, 
partly because of the indefiniteness which lies in the 
particularity of both premises, and partly because of 


the negative nature of both premises ($ 106), no valid 
inference results. 


Since the ground of the proof of the invalidity lies in the 
indefiniteness of the parts of the spheres, it follows 


can apply to it the axiom of the 
lar judgments 


that one 
paragraph on those singu- 
whose subject is something denoted by its uni- 
versal notion, but is an individual left indeterminate, i.e. 
those singular judgments which ($ 70) fall under the wider 
notion of the particular. This indefiniteness, however, has 
nothing to do with those judgments whose subject is an indi- 
vidual designated individually (e.g. by a proper name), i.e. 
with those which are not to be reckoned individuals but 
generals, 


Aristotle expressed the axiom that no syllogism can be without 
a universal premise in these words: ! 


τὸ καθόλου ὑπάρχειν. Later logicians have more universally 
based the proof which Aristotle adduced in examples of in- 
dividuals only, on the relations of the spheres. 


The forms of combination which must be rejected according 
to this rule, besides 0 0, which has been already eliminated by 
the rule of the preceding paragraph, are the three following :— 


3 Ψ - A a 
ev ἅπαντι συλλογισμῷ δεῖ 


11 οἱ 
io 
So that according to this the following nine forms remain :— 
aa ea ia oa 
a0 ie 
ai ei 
80 


all of them do not lead to valid conclusions. 


I Anal. Pr. i. 24. 


cc 2 











3 


88 § 108. The Combination of a Particular 








§ 108. Lastly, in all figures the combination of a par- 


ticular major premise with a negatwe manor premise does 


not tead to a valid inference. 


and the minor premise unw 


notion 
form its subject or predicate, is connect 


definite part of the sphere of one extreme A (cf. § 71; 
cf. 107), but, according to the minor premise, 1s com- 


pletely 
the following Schema :— 


For— 


(a) If the major premise 18 particularly afirmative, 
ersally negative, the middle 


M, according to the major premise, whether it 
ed with an in- 


na . = ou 
separated from the other extreme B, acco! ding to 


Here there is a conclusion whose subject is A and whose 


predicate is B: (At least) some A, viz. those which 


coincide with M, are not B, because it 1s quite separ 


rat “om 
from all M, and must, therefore, also be separated fr 
those A which coincide with M. There is no conclusion, | 


hose subject is B and whose predicate 1s A, | 
ing to the | 


however, W 
because it remains undetermined, accord 


premises, whether 
remaining A, and therefore from the w 
notion A, or partly coincides with it, or finally fal 


ated | 


B is also quite separated from the | 
hole sphere of the} 
ls | 


| 
| 
| 
| 
| 


Major Premise with a Negative Minor, ete. 











389 


wholly within it. In other words, it is quite undeter- 
mined whether no B are A, whether some & are A and 
others are not, or, lastly, whether all B are a. The 
particular negative conclusion which is actually drawn: 
Some A are not B, does not, according to the general 
rule (ᾧ 88), admit of Conversion. In order to reduce 
these two relations, the validity of the inference from A 
to Band the impossibility of an inference from Β to A, 
to one short general expression, that logical terminology 
must be applied, which designates the two extremes (A 
and B) in their distinction from each other according to 
the presupposed universal form of the conclusion, whose 
possibility is yet to be tested. This terminology calls 
that notion, which is to be the subject in the conclusion, 
the minor term (S), and that which is to be the predi- 
cate, the major term (P); and in this way determines 
the major and minor premises. According to this ter- 
minology, if the universal form a » is taken for the 
conclusion, and the validity of such an inference, as well 
as the more determinate form which the valid conclusion 
must take (whether a, e, i or o), is tested, A is the 
minor notion (S), B the major notion (P), and that 
premise which contains the A is the minor premise, and 
the other the major premise. Now if, according to 
the presupposition, the. premise with A is particularly 
affirmative, and that with Β particularly negative; the 
valid inference (some A are not B) is here attained 

from a particular affirmative minor premise and a uni- 

versal negative major premise. But if the opposite 

irom BA is laid down as the basis of the conclusion, 

and the investigation carried on, whether a similar con- 














390 ὃ 108. The Combination of a Particular, ete. 





clusion in any more definite form (a, e,i or o) results 
from the premises, then A may all the more be de- 
signated the major term (P), and the premise which 
contains A the major premise, and Β the minor premise 
(S), and the premise which contains B the minor pre- 
mise. This testing has now shown that no valid con- 
clusion of the form B A results from the above premises. 
The result may also be expressed: The combination of 
a particular affirmative major premise (the premise 
with a) and of a universal negative minor premise (the 
premise with B) does not lead to a valid inference. And 
this is what was to be proved. 

(b) If the major premise is particularly negative, no 
valid conclusion results because of the negative character 
of both premises (§ 106). 

(c) If the minor premise is particularly negative, no 
valid conclusion results because of the particularity of 


both premises. 


This demonstration could have been reduced to a shorter 
form by the immediate introduction of the signs Sand P. It 
seems important, however, because many misunderstandings 
have owed their origin to these designations, to state thoroughly 
the actual relation of the case, and to prevent the charge 
(however unfounded) of an hysteron-proteron, which might 
have been made. If the artificial expressions: major notion, 
minor notion, major premise, minor premise, are to be avoided, 


the paragraph might be headed: from the combination of 


a particular and of a negative premise no inference of such 
a form can result, that the notion, united in the particular 


premise with the middle notion, is the predicate of the con- | 


clusion, and the notion united with the same in the negative | 
But there is 00 | 


tenable reason for avoiding that terminology. Etymology | 


premise is the subject of the conclusion. 


δ 109. Lhe First Figure in the Stricter Sense. ete. 391 





does not define the meaning of scientific expressions ; Defini 
tion does. According to this definition the heading of shin 
paragraph only asserts in a more precise form what the axi a 
just enunciated does; for it substitutes their definitior for 
~~ technical expressions under consideration re 
sensi teathetin Gaedituk of tor tn oa ee 
| jected, viz. ie, io, oe, andoo 
if the last three were not already excluded by the PER 


rules. 61 re 
| There is, therefore, added to the earlier eliminations 
one new one, viz. :— 


16 
So that there remain the following forms only :— 
aa ea ia oa 
ae 
ai ei 
ao 


" amen these eight forms of combination of the premises 
ere is none which would be absolutely incapable of leadi 
to a valid conclusion in any figure, and therefore mu = 
universal reference, be eliminated. But some of the ei ht 
forms of the preceding schemes are to be excluded in oan ἔξ 
the figures according to the especial rules of these eae ; 

The rules for the relation of the form of a valid EEE 
En pi the preise (e.g. to the rule: “ conclusio sequi- 
καὶ Ρ rtem ebiliorem ) must, if they are to be proved with 
ull logical strictness, be established on a comparative survey 


of the individually vali 
y valid modes of inf 
to be mentioned below (§ 118). inference, and are therefore 


| $ 109. Lhe First Figure in the stricter sense, or the first 
division of the first principal class of the F. En Figure i 
the wider sense, does not lead to a valid we; Ss. 
the major premise (M P) is particular and when the 
minor premise (S M) is negative. For— 


(a) When the major premise is particular and afirma- 














392 ὃ 109. The First Figure in the Stricter Sense, ete. 





tive, or particular and negative, then the predicate P is 
affirmed or denied of a part of the sphere of the middle 
notion M; and the minor premise, which in this case 
according to the general rules ($$ 106-108) must be 
universally affirmed, asserts that the sphere of 5 falls 
wholly within the sphere of M, without determining in 
what part of the sphere of M. Hence it remains uncer- 
tain whether § falls within that part of M of which the 
major premise has affirmed or denied the predicate P, 
or within the other part of which nothing has been 
determined, or partly within the one and partly within 


the other part of M. 


() » 


Therefore the relation subsisting between S and P also 
remains quite indeterminate. 

(b) When the minor premise is negative, then, whether 
it is universal or particular, S is wholly or (at least) 
partly separated from M. But M is subsumed under 
P by the major premise, which must be both affirmative 
(§ 106) and ($ 108) universal, while it is left undeter- 


mined whether, and how far, the sphere of P stretches 


beyond that of M. Hence it remains also indeterminate 
in what relation S stands to P, and no conclusion can 


$ 109. Lhe first Figure in the Stricter Sense, ete. 





result from the form SP. The Schema for the case 
relatively conformable to the least indeterminate, and 
5 ° ᾿ ‘ . : a ' 
in particular premises, the case always possible, is the 


following :— 
(+) 


: OG) «(ρα 


Hence it may happen that no S is P, and also that some 
S are P, others not, and, lastly, that all S are P 
Hence nothing definite can be asserted of the relation 


of S to P. 


If we look on S and P as indifferent signs only of the two 
extremes, and use them as A and B, the following valid in- 
ference will always result from the last Schema: (At least) 
some P (those namely which fall within the sphere of M) are 
not S,or: Some B are not A. But this conclusion does not 
properly belong to the First Figure in the stricter sense, or to 
the first division of the first chief division, but to its shamed 
division, or to the so-called Fourth Figure. For the first P 
or Bin relation to this form of the conclusion is now babies 
the minor notion (S), and the first S or a the major notion 
(P). Hence, if the first minor notion is become the maior 
notion, and the major the minor, the external position or == 
cession may remain unchanged, and the middle notion is now 
predicate to the major, or is in the major premise, and subject 
to the minor, or in the minor premise. Consequently the 
Fourth Figure (in the moods Fesapo and Fresison) arises. 

The forms of combination, which accordingly fall outside of 














394 § 110. Zhe First Mood of the 





the First Figure, are ia, 04; 40, a0. Hence there 
remain the four following only :— 


aa ea 
ai ei 
It must now be shown that these necessarily lead to valıd 


inferences. 


$ 110. The First Mood of the First Figure has the 
form 8 8 a, i.e. its premises are a universal affirmative 
major premise, a universal affirmative minor premise, 
and its conclusion is likewise a universal affirmative 
judgment. Hence the universal Schema of the First 


Figure: 





takes here the more definite form— 


Ma P 
S aM 


5. ae » 


This mood bears the scholastic name Barbara, which 
is formed so that its initial letter, as the first con- 
sonant of the alphabet, shows it to be the first mood, 
and the vowels of the three syllables (a, a, a) denote in 
their succession the logical form of major premise, minor 
premise and conclusion. The other letters are inserted 
for the sake of euphony. The comparison of spheres 
shows the validity of this mood. For every universal 
affirmative judgment presupposes (according to $ 71) 
one of two relations of spheres whose Schema is— 





First Figure—Barbara. 





i.e. the predicate B is always present where the subject 
A is, while it is left undetermined whether other ex- 
istences besides have or have not the same predicate. 
Hence the Schema of the two combined judgments— 
= & F 
" ἃ Ν 


is the following :---- 


It remains generally undetermined which of these four 
relations belongs to a given single example; but since 
in every one of the four possible cases such a relation 
exists, that the predicate P belongs to every S, the 
conclusion— 

3 ΔΤ 


follows in a strictly necessary way from the premises; 
which was to be proved. 

This is the mood which is used most frequently, and 
in the most important cases, in the sciences and in 
common life, though commonly in an abbreviated (en- 
thymemic) form, and without logical consciousness. 


The comparison of spheres by means of circles as little pre- 














396 § 110. Zhe First Mood of the 





supposes that the notions compared are made substantives, as 
it did in the case of single judgments (see above, § 71). The 
different ways of apprehending, represented by Aristotle, Kant, 
and Trendelenburg (see above at ὃ 105), may exist coordinately 
with it. 

The four following syllogisms may serve as examples of the 
four relations of extent possible. The comparison is made 
easier and more evident by the fact that they have been so 
chosen that the middle term (M) (viz. Triangles, in which the 
angles of the one are equal to the angles of the other each to 
each) is the same in all of them. The premises will take the 
position which is here the most natural, the minor premise 
always precedes the major. 

1. Those triangles, into which the right-angled triangle is 
divided by the perpendicular from the vertex of the right 
angle on the hypothenuse, are triangles whose angles are 
equal each to each. All triangles whose angles are equal each 
to each other are figures which are similar to each other. 
Hence those parts of the right-angled triangle are figures 
which are similar to each other. 

2. All triangles, the relations of whose sides are equal each 
to each, are triangles whose angles are equal each to each. 
All triangles whose angles are the same each to each, are figures 
which are similar to each other. Hence all triangles, the rela- 
tions of whose sides are equal each to each, are figures which 
are similar to each other. 

3. Those triangles, into which a right-angled triangle is 
divided by the perpendicular from the vertex of the right angle 
to the hypothenuse, are triangles whose angles are equal each 
to each. All triangles whose angles are equal each to each, 
are triangles in all respects similar. Hence those triangles 
which are made by that division of a right angle are triangles 
in all respects similar. 

4. All triangles, the relations of whose sides are equal each 
to each, are triangles whose angles are equal each to each. 
All triangles whose angles are equal each to each, are similar 
to each other. Hence, all triangles, the relations of whose 
sides are equal each to each, are similar to each other. 


First Figure—Barbara. 





The second and fourth cases occur more especially when the 
middle notion is an individual notion, and when either a 
universal or an individual predicate is attached to it in the 
major premise. The first German teacher of the differential 
calculus is Leibniz. Leibniz is the author of the system of 
Monadology. Therefore, &c. He who founded syllogistie 
was Aristotle. Aristotle was the most influential tutor and 
trainer of Alexander the Great. Therefore, &c. 

In order to show the significance of this first mood of the 
First Figure in scientific knowledge, the following examples 
from the different sciences may be given. 

Direct mathematical demonstrations for affirmative theorems 
are given exclusively in syllogisms of this mood. The logical 
analysis in such demonstrations and attempts at demonstration, 
where an oversight easily occurs, has a special interest, and 
we will therefore choose as an example a course of reasoning 
having to do with the well-known eleventh axiom of Euclid. 
This axiom asserts, that two straight lines (AB and CD), 
thought as infinite, in the same plane, which are intersected by 
a third line (E F), so that the two interior angles on the one 
side of the intersecting line (BG H and DHG) are together less 
than two right angles, must intersect each other on this side. 


E 





It was early recognised that this axiom is not so evident as 

2 others. It does not assert something about a self-contained 

sure, which is at once presented in the very intuition. In 
16 axiom that two straight lines which cut each other diverge 
aually from the common point, it is only requisite for 

















aS = 


fi 
Be nn 


398 § 110. The First Mood of the 








intuition to follow the construction from distance to distance, 
each time as far as it directly witnesses for the assertion, in the 
faith that what now holds good will hold good from this dis- 
tance onwards; but more is needed here. It is demanded that 
an intersection which, in a very small divergence of the sum 
of the interior angles from two right angles, does not exist 
at a very great distance, does exist at a position lying at an in- 
definite distance further off, where immediate perception can- 
not be sure that it is correct, while the axiom is recognised to 
hold good for all cases on the ground of this intuition. This 
undeniably requires proof. The eleventh axiom of Euclid 
may be divided into an axiom and a theorem annexed. It may 
be taken as an axiom, that if any third line (E F) which in- 
tersects the two lines (I K and c D) makes the corresponding 
angles equal, then any other line (6 L) which intersects the 
two makes the corresponding angles equal. From this follow 
the theorems, that the external angle of a rectilineal plane tri- 
angle is equal to the sum of the two interior and remote angles, 
and that the sum of the three angles of a triangle are equal to 
two right angles. It also follows conversely that if one of 
these axioms be taken to be an axiom, the axiom from which 
they are deduced would also follow from them. On the basis 
of these axioms a stringent proof may be led for what is asserted 
in the eleventh axiom of Euclid. But the proposition given, 
which approaches nearer the axiomatic character than the 
eleventh axiom of Euclid, is too complicated to be considered a 
perfect axiom. What it affirms is conditioned by the nature 
of the straight line and of the angle. The true element, to 
which the special task in the construction of the axiom is to be 
referred, must lie in this nature. But this reference is accom- 
plished most conveniently by the introduction of a notion (new 
to the representation of Euclid)—the notion of direction. The 
straight line is defined to be a line originating by the motion 
of a point in a constant direction, the angle is defined to be the 
distinction of directon of two straight lines intersecting each 
other, and parallels are defined to be lines of the same direction. 


1 It is to be understood, that the notion of direction, which is con- 


First Figure—Barbara. 399 





On the basis of this definition it is to be proved, that the 
line A B, if the sum of the angles BG H+DH6@< 2 R, 
must at an indefinite distance intersect the line c p on the 
side of Ε F on which B lies. 

Let the straight line 1 K be drawn through the point ¢ in 
the same direction as CD. The following syllogisms may 
then be constructed :— 

1. Like directions have like distances of direction; the direc- 
tions of 6 Καὶ and HD, of GH and HF, are like directions; 
hence they have like distances of direction, i.e. angle Καὶ α H= 
DHF. 

2. Adjacent angles are together equal to two right angles; 
the angles DH F and Ὁ Η α are adjacent angles; therefore 
DHF+DHG=2R. 

3. Equal magnitudes may be substituted for each other; 


ditioned by the tendency of the motion (but is not identical with the 
notion of straight line), is not itself capable of a definition of such a kind, 
that proofs led in the way of Euclid may be built on it. The argument 
has rather the character of a philosophical explanation of notions, 
and in mathematical consideration falls short of an axiomatic. This 
will not be concealed by a notion newly introduced, but will be intro- 
duced in the most elementary form possible. The course of thought: 
the angle is a quantity of turning, therefore advance in a straight line 
is without influence on the sum of the angles, therefore the sum of the 
external angles of a triangle = 4 Β, and the sum of the angles of a 
triangle = 2 rR, is essentially the same as the above. A demonstration 
built on this course of thought would have this preference to the one 
given above (which may be expressed in fewer syllogisms), that the 
notion of equality of direction may be used without definition as some- 
thing immediately understandable only when applied to the constancy 
of the direction of the motion of a point advancing in a straight line, 
and of the motions of two lines proceeding from different points. If it 
is used with this application, the attribute of the equality of the angle 
which the lines make with an intersecting line is contained in it, and 
80 is the axiom referred to above, that the angles which the lines then 
make with any other line intersecting them are equal to each other. 
This axiom (aequipollent with the proposition that the three angles of a 
triangle = 2 R) is the natural prius of the eleventh ‘axiom’ of Euclid. 




















400 § 110. The First Mood of the 





the angles K G Hand DH F are equal magnitudes (according 
to 1): therefore they can be substituted for each other. 

Let us substitute accordingly in an inference like No. 2 
KGHforDHFthnKGH+DHG=2R. 

4. According to the hypothesis BG H+DHG<2R. If 
now the proposition about substitutions is taken as the major 
premise, and the result reached above, that KGH+DHG= 
2 R, is taken as the minor premise, and the conclusion drawn, 
it follows that BG H+DHG<KGH+DH64. 

5. The subtraction of an equal from a less leaves a less. 
The subtraction of the angle D H 6 from the sum of BG H+ 
pu is the subtraction of an equal from a less in com- 
parison with the subtraction of the angle D H G from the sum 
of KG H+pD 44; hence a less remains, 1.6. BG H< KG H. 

6. Two unequal angles in one plane, which have the vertex 
and one line common, and lie on the same side of the common 
line, must so lie that the other line of the lesser angle projects 
from the vertex between the two lines of the greater. (For 
the greater difference of direction corresponds to the wider 


turning of the side of the angle around the vertex, and the ᾿ 


smaller to the smaller.) The angles Β 6 Hand K G H are two 
angles of this kind. Hence they must lie so that αὶ B falls 
between G H and α κ. (The diagram shows it immediately: 
It could not, however, as self-evident, exempt us from the 
necessity of a proof.) 

7. Vertical angles are equal to each other: the angles 
p HF and cH Gare vertical angles, and therefore equal to 
each other. 

If K @ H were substituted for D H F (according to 3) then 
we should have KG H=cH@. And since the propositions 
which establish the conclusion contain nothing which would 
not be quite as true for every position and distance of lines of 
the like direction (I K and c D) and of the intersecting one 
(Ε F), this result may be universally expressed: Reciprocal 
angles in lines of the like direction are equal to each’ other. 

8. Reciprocal angles in lines of the like direction are equal 
to each other; the angles KG L (KGL,KGL,, &c.) and 


First Figure— Barbara. 401 








HLG (H L, G, HL, 6, &c.) are reciprocal angles in lines of a 
like direction, and therefore of a like direction 

The points L,, 1,9» L,, &c. may be so defined that HL. -- 

— - τ 

HG, Τὴ Τρ ΞΞ Τὴ G, L, 15 ΞΞ 14 G, and so on ad infinitum. We 
may then further conclude :— 

k 

9, Isosceles triangles have equal angles at the base. (The 
> ἢ of this is independent of the eleventh axiom of 

uclid.) The triangle H L, G is isosceles. Hence it has at 


the base (6 L,) equal angles, i.e. the angles HL, G=HGL 

Hence it follows that the angle HL,G=L, GL. HL = 

L, 6 L,, &c. νυ. 
r . . 

= 2 magnitudes which are equal to a third are equal 

to each other. Th 3 K CGI 

RL. e angles KGL,KG L, KGL,, &c., and 
ae » L, GL,, &c. are two quantities, which are 


equal to a third (vi 
q oa third (viz. HL, G, HL, 6, H L, 6, &c. according to 


8 and 9), 
2 oo Hence they are equal to each other, each to each : 
igh GL, Ei =p K6L=LGL, KGL,=L,6 Lz, &c 
ther words: the anole k q 4 ᾿ 
gle Κὶ G Hand the angle KG L(KG 1)» 


KGL, KGL,, &c.) are : i 
"a 2 3 ) always bisected by the next straight 


ll. TI 
16 sum of the series ὁ 1.2 2.4... ., 


magnitud ifferer j 
| mag es be given, the difference of the sum from unity 


in infini ' 
| Eu; advance of the series must continually become 
ess. 

e angles H G L,, H 6 L,, &c. are the successive sums 


of angles (H G L,, L, 6 1,» &c.) which are parts of the angle 
HG K according to the progression 4, 4, 1, τίς» &c. (accord- 
we 10). Hence they approach the unity or the whole angle 
is angle (HG K) in such a way that what and however 
small a magnitude of an angle (Κ @ B) may be given, th 
difference of the angle Η GL, from Η G K must 2 ἡ 
= magnitude KGB. Let us denote the point on the line 
D (to be thought of as infinite) where this diminution com- 
mences, G L,, it follows that HG L,>HGB. 
12, If the major premise of 6 be applied to this case, then 


DD 

















402 





§ 110. Zhe Fürst Mood of the 








in the same way it follows that the line α B must fall between 


G H and G Ly. 

13. An infinite straight line can procee 
bounded on all sides in the same plane on two sides only by 
means of intersecting the boundaries. The line AB is an 
infinite straight line, which (according to 12) lies partly 
within the triangle H Ly α which is bounded on all sides. 
Hence it can only pass through it on two sides only by means 
of intersecting the limits. 

The one intersection is at G, the other not yet determined. 


14. Two straight lines which do not quite coincide can have 
GB and G H are two such straight 


d but from a figure 


only one point in common. 
Hence they can have only one point in common (the 


lines. 
The like holds good of G B and 


point G only, and no other). 
ch. 

15. The infinite straight line @ B (or A B), in order to 
go through beyond the enclosed space of the triangle H L, € 
τὴ the direction of B, must intersect one of its three sides in 
this direction (according to 13). But it cannot (according to 
14) intersect in this direction G HorGL. Hence it must 
intersect the line H L, (or C D); which was to be proved.' 


1 If the major premise of 13 is not used, it must be asserted further 
that the straight line L,_, (to be thought of as infinite), if it is turned 
about the point 6 at the coincidence with 1, in the plane determined 
by the three points G, Ly4 and L,, may pass through all points of the 
line L,_, L, and also through all points of the triangle α Ly_, Ly, and 
consequently may have a second point besides ἃ, common with the line 
α B (or A B), and then must wholly coincide with it, so that its point of 
intersecting, Ly-1 Lx: belongs also to the line a B, and hence that this 
sntersects © Ὁ; which was to be proved. 

In mathematical reference the author's article on the principles of 
Geometry, scientifically explained in the Archiv fur Philol. und Pade- 
gog. (founded by Jahn), xvii. pt. i. 20-54, 1851, may be compared. ‘The 
notions here applied are there explained in their more universal scientific 
connection. This treatise was republished with an introduction altered 
by myself in a French translation in Joseph Delboeuf’s Prolegomenes 
philosophiques de la Geometrie, pp. 269-305, Liege, 1860. 


foundation of geometry on 


Delboeuf’s | 


the one fundamental character of space | 


| 
| 
| 
| 
| 
| 
| 


First Figure—Barbara. 403 





Br EEE under 15 is of a form which cannot be 

o the mood Barbara (a form of a disjunctive kind), and 

that under 14 is to be added in so far that the ‘only’ ¢ ae 

the point G, and no other ᾽) implicitly contains a Hes Es Be 
g \ 


ke ent : that the form is independent of the magni- 
eae bd be united to every magnitude (which may be 
scientific apprehensio = ee a 
of space, but to the un . an on ed 
ion. Se eis ee τας 
Στ ἡ ai rift für Phil. xxxvii. 
die en — en εν ohn Prince Smith, Ueber 
rg } in, 1860. Cf. further H. Helm- 
pag rath on at the Zoe of Geometry, in the Nachrichten 
where, hr Hikes e = ales age een ee 
86 ες : £ lisch. der Wissensch. zu Göttinre 
er a = simple facts is enumerated as amounts en 
Riemann defines u nn or ee eek 
re nensions as an n-fold extended " 
er : Τῷ such an one that the individual in it is determined ΘᾺ : 
Weine e magnitudes (co-ordinates). The capacity of space for 
= eo mn existence of steady bodies. By means of 
points can be brought we ne Penge oo 
τὸ nate gruence. 118 15 independent of th 
art 2 ee = a congruent systems of points and of the sc 
wer z ss are rought to each other. Ifa steady body turns 
depends only a ieee τῶν and these are so chosen that its position 
biting Rania amg independently changeable, then the turning 
en ee to the point of beginning. Space has three 
cise = fs aa extended. In the above-mentioned 
perimental facts a : a. Be ee RB WE ΜΝ on 
absolutely strict v “ni ΜΝ ἊΣ ang axiomatically to be of an 
the testimony of the en ee = - ra 
not fixed at any point, sia ἐν ni hia steady body: 1. If it is 
2. When fixed at a point, cannot be an oe 
at a second point, cannot eben all the <a en en 
aint 10tions which are still pos- 
ΩΝ, ed Sams ἊΝ _ but can still always be moved warn 
es p Ν which stand in unbroken connected succession 
each other and the two fixed points remain unmoved) ; 4. If it 


Dp 2 
































404 § 110. Zhe First Mood of the 





All the syllogisms of the first thirteen numbers fall under 


the first mood of the First Figure. 
This syllogistic concatenation is the spinal cord of mathe- 


matical demonstration. The mathematician shortens the form 


is fixed at one of the points hitherto remaining moveable, all motion is 
taken from the body. 

In the treatise by Tiberghien, a follower of Krause (Logique, la Science 
de la Connaissance, Paris, 1865), the anti-Kantian opinion expressed 
in the above-quoted tractate, that the certainty of mathematical axioms 
is compatible with an empirical origin of the conception of space, is 
combated. I there said, that Kant’s demonstration for the a priority of 
the intuition of space is only an indirect one, which is grounded on the 
disjunction : given by experience or independent of all experience (em- 
pirical or ἃ priori); and the demonstration is fallacious because of the 
incompleteness of the disjunction, for there is a third possibility, viz. 
the intellectual working up the empirical data according to logical laws 
without the ἃ priori (i.e. independent of all experience) elements of 
knowledge. If we do not reach mathematical knowledge by direct 
observation, it does not follow that it is absolutely independent of all 
observation. The mathematical fundamental axioms are partly analy- 
tical judgments (§ 83), but are partly, so far as they are synthetical 
judgments, like physical judgments, e.g. the law of gravitation based 
immediately on observation, the geometrical on the observation of the 
relations of space, and the arithmetical on the observation of objects of 
the same kind leading to the notion of number. From these funda- 
mental axioms the theorems are derived by means of a syllogistic 
deduction, which does not follow purely subjective laws, but is 
founded on the presupposition of an objective arrangement, which our 
thinking only reproduces, and this presupposition itself rests on the com- 
bined external and internal experience (cf. §§ 28, 41 ff, 75, 81, and 
several of the remarks to δὲ 137, 138 ff.). Tiberghien answers 
(p. 244 f.) with the question, Why does Kant leave the third possibility 
unnoticed? and answers it thus: ‘It is because the critique of pure 
reason had shown that there is no knowledge without elements a priori, 
and that thus the elaboration proposed is manifestly absurd.’ But this 
answer involves an error in reference to Kant’s actual course of demon- 
stration. It is only necessary to read Kant’s work to be convinced that 


Kant proceeds upon this disjunction in his reasoning, that he employs 


it as premise, and not, as Tiberghien asserts, as a result or conclusion οἱ 


a demonstration independent of it. The third possibility is to be called 


First Figure—Barbara. 405 





of expression, but the syllogistic form of thought cannot b 
removed without destroying the force of the ων ρῶν, 
itself. ᾿ ἢ 
Physics also can explain particular phenomena from syllo- 
gistic rules only in a syllogistic form of thought. Every appli- 
cation of a mathematical formula to a ren case is al 
means of a syllogistic subsumption of the special under a uni. 
versal relation of magnitude or situation. The province of the 
syllogism, and more especially of the mood Barbara, in Physics 
extends beyond that of the mathematical ficekole, The law 


that the warm body must radiate part of its warmth out through 
the atmosphere towards a colder surrounding it, if it is not 
separated from it by protecting media, and nase grow cold 
adds to our meteorological knowledge by means of ayliegiekie 
subsumption, without being brought to a mathematical Fortis, 


an ‘ evident absurdity,’ if the subjective presupposition is thought to be 
an unalterable truth, that all orderly arrangement has its ee in our 

selves only. But this itself is first deduced from this disiunstien, 
whose completeness is what is questioned, and therefore the dite 
undeniably proceeds in a vicious circle. If Tiberghien on his sid 

believes this hypothesis to be controvertible, there "τ even “ee a 
pearance of justice for that designation. Kant’s rejection of ‘i 
weightiest of all objections which have been raised against his doctrine 

by a mere jest (‘ Ex pumice aquam!’ Kr. d. pr. V., pref.), whose a : 
plication involves the Kantian hypotheses, may be ER and -: 
cusea from Kant’s subjective isolation at his own stand-point, but not 
accepted. Lastly, so far as the infinitude of space goes whe Tiber- 
ghien lays so much stress on, this can only be wiiddeerntocd by us in the 
negative sense, that the possibility of advance to any other place is not 
taken away, and only this notion is mathematical. Reimann u H 

Helmholtz, in the above-quoted articles, recognise the empirical basis of 
Geometry as settled. Cf. Beneke, Syst. d. Log. ii. 51 ff. 

[ Another side of the Logic of Geometry stated in this paragraph, that 
the major premise so defines the geometrical notion that the ‘saison 
trom the construction may be dispensed with in the proof, is combated 
by Prof. W. R. Smith in two papers read before the Royal Society of 
Edinburgh (Transactions, vol. xxv.), ‘On Mr. Mill’s Theory of Geo- 


mean: Reasoning,’ and ‘ Hegel and the Metaphysics of the Fluxional 
aleulus.” Cf. Translator’s Preface. | 








— EE a TEE eT ne = 

















rn 2 ghee ch 4... A ᾿ Zum - 
Sasse = = — - —- 


~~ - - - “0: 


| : 
tal 
1: N 
᾿ Mm 
Eu 
t 
2 
18 Uo 
> | 
TRE 
τ 
ie m 
ny 


406 § 110. Zhe First Mood of the 








The superficies of the earth by night, under a clear sky, is 
warmer than the surrounding space, and is not separated from 
it by a cloud-covering protecting it from cooling. It there- 
fore must radiate a part of its warmth, and become cooled (until 
the warmth of the sun makes reparation). The explanation of 
the formation of dew rests on the syllogism: Every cooling 
object whose temperature is below that of the so-called point 
of dew, attracts to itself out of the atmosphere a part of the 
watery vapour contained in it, and causes it to precipitate 
itself on it; the superficies of the earth, and especially of 
plants, are colder in clear nights than the atmosphere, in 
consequence of the radiation of the heat to- the space around; 
and, therefore, when the cooling exceeds a certain limit, they 
attract a portion of the watery vapour contained in the atmo- 
sphere, and make it precipitate itself on them. 

The application of grammatical laws to individual cases is 
a syllogistic process of thought. The verbs (verba sentiendi 
et declarandi) which denote an intellectual activity (the recog- 
nition an existence of what is) require in Latin the construction 
of the accusative with the infinitive ; persuadere with the 
meaning to convince (that something is) denotes an intellectual 
activity, and requires this construction. Verbs which refer 
to a striving (after something which ἐ8 to be) take the con- 
struction of ut; persuadere in the meaning of to persuade 
(to do something) belongs to this class, and, with this meaning, 
takes the construction of ut. 

The like holds good of the application of the laws of justice. 
Theft is the crime in which a moveable thing belonging to 
another is taken from his possession or custody. The deed 
which this accused person has done is a crime of this kind. 
Therefore itis theft. Theft requires a severer punishment than 
the appropriation of something found (which was not in the 
possession or custody of another, if the former possessor had 
lost or abandoned it). . The deed done by this accused person 
is theft. Therefore it- requires severer punishment. In the 
application of a law to a given case the major premise is 
established by laying down the law ; the minor premise has t0 


First Figure—Barbara. 407 





do with facts, and is found out by actual sight, avowal, tes- 
timony or circumstantial evidence. If an eathientic target 
tation lies between the law and its enforcement, then in this 
case the law is the major premise, and a delivery of the court 
by which the meaning of an expression used in the law is 
stated (e.g. whether the erroneous subjective view, that sila 
thing may have happened which has not happened, be an 
‘opinion ’ in the sense of law or not), is the minor premise, and 
a rule directly applicable to one of the individual cases present 
(or directly excluding this applicability) is the conclusion. 

In the province of Ethics the particular is known from 
the general syllogistically, however much the expression may 
despise syllogistic prolixity. This prolixity indeed is not 
required, because the ethical relations lie so near the uni- 
versal human consciousness. But the course of ethical think- 
ing is syllogistic, if we, e.g. affirm of a definite person, whom 
we have known to be faithful to duty, that he is worthy of 
esteem. - For we subsume the individual case under the uni- 
versal law that fidelity to duty establishes the ethical claim to 
esteem. 

The like holds good of the understanding of hestorical phe- 
nomena. Besides the explanation given by Schiller of the 
vehemence and length! of the Thirty Years’ War—that in re- 
ligious wars, and more especially in later times, the individual 
takes his side from personal conviction—the following example 
may bear witness to the force of this form of thoughé, Those 
individuals who have freed the elements of culture, separately 
acquired by the noblest and best endowed peoples of antiquity 
from their national limitations, and made them extend over all 
peoples of the earth capable of civilisation, are among the men of 
antiquity who are of most world-wide importance. Men who re- 
cognised the elements universally true for man in the rich treasury 
of Grecian Art and Science, of Roman law and policy, acquired 
by the labour of centuries, and, in a still greater degree in 
religious ideas jealously guarded by the Jewish people, who 
have freed their eternal truths from the temporal and transient 


! Already quoted, $ 101. 



































᾽ 
ii 
Ϊ 
i 
ἢ 
| 
tah 
¥ 
i] 
f | 
ἢ] δ] 
{ΠΝ Ἢ 
Hi} 
ar 
Ἢ 
1 
oF 
Pee 
{π᾿ 
1 
ἘΝῚ 
iu 
i 
| 4 
| ΠῚ 
Ian 
= u 
He | 
vi 
Hai i 
1 44 
ΕἸ ΜΝ ἢ 
bp 
tin 4 
it | 
en | 
un 
+ | 
ve 
ΕΠ ἢ 
| 
’ 
1 








408 § 111. Zhe other Moods of the 





veil of national restriction, who have advanced them to a 
new and purer position, and have prepared the way for their 
universal diffusion,—they are, each in his province, men who 
have freed elements of culture, &c. Hence, they are the men 
of antiquity who are of the most world-wide importance. If 
this conclusion is referred to individual persons, in whose 
effects on the history of the world that character has shown 
itself, this reference in its logical form takes the same mode 
of inference. If the major premise of the first syllogism re- 
quires verification, this is to be done only in a like syllogistic 
form of thought, viz. by presenting a universal law of deve- 
lopment, which mankind, as one whole ethical organism, must 


obey. 


§ 111. The three remaining moods of the Fürst Figure 
in the stricter sense have the forms eae, aii, ei o, and 
take the names Celarent, Darii, Ferio. In these names 
the place in the alphabet of the initial consonant signi- 
fies the order of the moods, and the vowels in their 
succession signify the characteristic logical form of the 
major and minor premises and of the conclusion. 

In the mood Celarent a universally negative conclu- 
sion (No S is P) is derived from a universally negative 
major premise (No M is P) and a universally affirma- 
tive minor premise (Every S is M), according to the 
following scheme :— 





The proof of the validity lies in the relation of spheres. 
If M is quite separated from P, and S contained in M, 
then S must be quite separated from P. 


First Figure—Celarent, Darii, Ferio, 


3 © 
© 


The mood Darii has the form — 
Ms? 
BE ae 
π 8 5 








The same relation of spheres exists here between P 
M, and those (some) S which are M, as in the aed 
Barbara (§ 110) between P, M, and all S. Hence it 
must be true of those (some) S which was there true 
of all S, that they are P. It remains uncertain of the 
remaining 5 whether they are Por not. If they are M 
they must also be P. If they are not M they may still 
be P, but they can also be not P. This easily results 


from a comparison of spheres. The conclusion has the 
meaning: At least some S are P. 


Lastly, the mood Ferio has the form— 
ma @ FP 
> £18 
> =. 2 
The same relation of spheres exists here between P, 
M, and those S which are M, as between P, M, and all 


Sin the mood Celarent (see above). Hence, as there 























eNO 


ie + 
———— 


: . — -- - - An eee RI κε λῶν ον σον σε x 
= Fee 3 = - = 2 En τ τ τ - = oe - ——— 
SS Le mem ποτ πο 

N a a x 


a 


So ΣΞ: 


—— en ΠΣ ὦ 


N 
| 
{ ἡ 

Ἕ 
4 

ha 
dad 
ἢ 

HP 
Ἵ! | 
ana 
IE 

if iy 
as 4 
is. Υ 
ih ἢ 











tl 
1 


er 





410 $ırı. The other Moods of the First Figure, etc. 





all S are not P, here at least some S are not P. It 
remains undecided of the remaining S whether they are 
P or not. Ifthey are M it follows that they are not Br 
If they are not M, however, then they can have any 
conceivable relation to P. Hence the conclusion has 
the meaning: At least some S are not P. 


No. 14 of the larger mathematical example in the foregoing 
paragraph is an example of Celarent. The ‘ only’ of the major 
premise contains the denial of a second common point. The 
following are other examples from other provinces of thought: 
(1) No form of knowledge, which corresponds to a peculiar 
form of existence, is of merely didactic value; Syllogism is a 
form of knowledge which corresponds to a peculiar form of 
existence (viz. to the real conformability to law). Hence the 
syllogism is not of-mere didactic worth. (2) What is involun- 
tary cannot be overcome by laws which entail punishments. 
Theoretical convictions are involuntary. Hence no theoretical 
conviction can be overcome by laws which entail punishment. 
(3) No just decision upon happiness is independent of moral 
restraint. The divine decision is correct. Hence it is not 
independent of moral restraint. 

Darii.—(1) What has proceeded from a pure moral con- 
sciousness must be allowed to be moral. Some deviations from 
the common rules of Ethics have proceeded from a pure moral 
consciousness. Hence some deviations from the common rules 
of Ethics must be allowed to be moral. In this case only some, 
those namely which are under the middle notion. In other 
examples the predicate of the conclusion is true of a part of 
the sphere of the notion of the subject conformable to the 
premises, but besides this of the other parts also, about which 
nothing can be inferred from the premises. All squares are 
rectilineal plane figures. Some (and on/y some) parallelograms 
are squares. Some (in fact however the other also) parallelo- 
grams are rectilineal plane figures. The value of this mode of 
inference, as well as of all other in the various figures, which 
are in the same case with it, is limited but not destroyed by 


$¥t2. The Second Figure, etc. 4it 








this indefiniteness. For everything is not indefinite, only that 
about which nothing can be concluded from the premises. It 
is always something gained to know that some S belong to P 
(or in other moods with particular negative conpbusinns, that 
some 8 do not belong to P). This gain is not to be despised 
because, so far as results from the premises, something further, 
the condition of the other S, remains unknown. * Too little’ 
may result for our desire of knowledge; but it does not follow 
that it is ‘ too little’ in the sense that the inference leads to a 
fallacious limitation of the predicate to some S. A fallacy can 
never originate by this mood of inference, nor by any like it, 
if correctly applied, provided only the meaning of the par- 
ticular judgment is strictly defined. 

Ferio.— No human weakness can belong to God. Some 
attributes imputed to the deity by mythology are human weak- 
nesses. Hence (at least) some attributes imputed to the deity 
by mythology cannot belong to Him. The remarks made upon 
the importance of the particular conclusion in Darii are also 
true in Ferio. 


§ 112. In the Second Figure, whose general scheme 
(cf. § 103) is the following: | 


(1) The major premise must be universal, and— 

(2) One of the two premises must be negative. For— 

1. If P and M are connected particularly (PiM, 
which corresponds to M i P) while the relation of the 
remaining part of their spheres remains undefined, and 
if S falls wholly within M (Sa M), then it remains 
uncertain whether S falls within that part of M which 
coincides with part of P, or within that part to which 
P has no defined relation, or partly in the former, 





























412 δ 112. The Second Figure, ete. 





partly in the latter. Hence nothing definite results 
about the relation of Sto P. If P, however, is par- 
ticularly separated from M (Po Μὴ), and if 5 falls 
within M (S a M), the consequence would then be that 
some P, viz. those which are not M, are also not S; but 
in this inference the particular premise would be the 
minor. On the other hand, nothing follows concerning 
the relation of S to P, for the sphere of P, the sphere 
of M, and, moreover, the sphere of S, which lies quite 
within M, may include, cross, or, lastly, wholly exclude 
each other, so that sometimes all S are P, sometimes 
some are but others not, and, lastly, sometimes no 5 
are P. All other forms of combination with a particular 
major premise are already excluded by the general rules 
(δὲ 106-108). 

2. If both premises are affirmative no valid inference 
can be attained, because both P and S wholly or partly 
fall within the sphere of M, and nothing results about 
their mutual relation. 


Of the eight forms of combination whose validity is not 
destroyed by the general rules ($$ 106-108), viz. : 


aa ea ia 0a 
ae 
ai 
a0 


ia andoa are rejected in the Second Figure, according to 
the rule of the universality of the major premise, and (besides 
ia) aa and ai according to the rule that both premises can- 
not be affirmative. Hence the four following remain: - 


ea ae ei a0 


Their validity is still to be proved. 


δ 113. Valid Moods of the Second Figure, ete. 413 





§ 113. The valid moods of the Second Figure have the 
forms eae, aee, eio, and aoo. They take the 
names Cesare, Camestres, Festino, and Baroco. In these 
names the vowels of the three syllables in their succes- 
sion denote the form of the major and minor premises 
and conclusion. The initial consonants refer to those 
moods of the First Figure to which the Schoolmen, 
following Aristotle, sought to reduce them in order to 
prove their validity. Some of the remaining consonants 
show the manner of this reduction (of which below). 


The comparison of spheres proves the validity of these 
moods directly. 


The universal scheme of the Second Figure— 
g M 
S M 
D Ρ 


in the mood Cesare has the more definite form— 





[he major premise asserts a complete separation of the 
᾿ > \ 
spheres of P and M, the minor a complete comprehen- 


sion of the sphere of S in that of M. The symbol is 
therefore— 








414 $ 113. Valid Moods of the Second Figure— 








In both cases the complete separation of M from P has, 
as a necessary consequence, a complete separation of the 
S which is in M from P. 
In the mood Camestres the scheme of the Second 
Figure takes the form— 
Yr aS 
Se M 


> ἃ F 





In this mood, when compared with Cesare, -P and ὃ 
have exchanged the parts they play; P lies wholly 
within M, S wholly without M. Hence follows that 
between M and P there is a relation of complete 


separation. 
An inference may each time be made from the same 


premises in Cesare and Camestres. The Conversion | 


of the (universal negative and therefore simply con- 
vertible) conclusion accomplishes the transference from 
the one mood to the other (which is not universally 
necessary, and is not the case in Darapti of the Third 
Figure), because the exchange of the major and minor 
premise conditioned by this has for its consequence a 
form of the major premise now present, which is 
changed when compared’ with the previous major pre- 
mise; the same is true of the minor. 
The mood Festino has the form— 
Ὁ ze 
Si M 
Bo F 


The proof of its validity lies in this, that those (some) 


Cesare, Camestres, Festino, Baroco. 415 





S which are M, must here stand in the same relation to 
P which is wholly separated from M, as all S in Cesare, 
that is (at least) these S, and hence (at least) some S 
are not P. (When all S are M, then all S are not P; 
when only some S are M, and others are not, then the 
two cases can enter; only some S are not P, while others 
are P, and all S are not P.) 
The mood Baroco has the form— 


ar: Ὦ 
> @ & 


πῃ. 
Here some S, those, namely, which are not M, stand to 
P, which falls wholly within M, in the relation of 
separation, as all S did in Camestres. Hence (at least) 
some S are not P. (When no S is M, then no S is P; 


but when only some S are not M, then sometimes only 
some S, sometimes all S are not P.) 


The following are examples of Cesare. It is inferred in 
the Platonie dialogue Charmides: Bashfulness is not some- 
thing thoroughly good; Modesty is something which is 
thoroughly good ; Hence Modesty is not Bashfulness. Aris- 
totle concludes :! the πάθη make men neither noble nor base, 
worthy of praise nor worthy of blame; the ἀρεταί do this; the 
ἀρεταί are not πάθη. Further: The affections do not rest upon 
purpose ; Virtues depend upon purpose; Hence they are not 
affections. In the same manner, Erdmann concludes :? The 
author of the essay on the relation of the Nature-Philosophy 
to philosophy generally* had not the consciousness that specu- 


I! Ethic. Nic. ii. 4. . 

2 Gesch. der neueren Phil. iii. 2, 694. 

ὅ In the critical Journal der Philos., edited by Schelling and Hegel, 
1802-3. 








416 § 113. Valid Moods of the Second Figure— 





lative Logic takes a special place in the list of philosophical 
sciences. Hegel, however, had this consciousness before the 


date of the essay. Hence Hegel is not its author. 
Camestres.— Aristotle shows! that the virtues are not δυνά- 


pes (original capacities, dispositions, or faculties) by the 
following inference: The δυνάμεις are natural gifts ; virtues are 
not natural gifts, but acquired properties or facilities; Hence 
they are not δυνάμει». Aristotle concludes :? Every knowledge 
of essence is affirmative; no conclusion in the Second Figure 
is affirmative ; Hence no conclusion in this figure is a knowledge 
of an essence. Further: Every knowledge of an essence is 
universal; no conclusion in the Third Figure is universal ; 
Hence the Third Figure does not lead to a knowledge of an 
essence. On the basis of the Aristotelian account of the Ionic 
natural philosophers, later historical criticism constructed the 
following criticism : According to the testimony of Aristotle,’ 
all those philosophers who define the one material principle as 
a mean existence between water and air have thought that 
things originate from this principle by condensation and rare- 
faction. According to the testimony of the same Aristotle, 
Anaximander thought that the particular kinds of matter arise 
from the primary matter not by condensation and rarefaction 
(but by repulsion). Hence, Anaximander (if both Aristotle’s 
testimonies are strictly accurate) does not belong to those 


philosophers who define the one material principle as a mean 
between water and air. The proof which historico-literary 


criticism has produced against the authenticity of Macpherson’s 
Ossianic poems may be comprehended, in so far as it rests on 
internal reasons, in the following syllogism : Every real natural 
poem is naive; those poems of Ossian which Macpherson pre- 
tended to discover are not naive (but sentimental). Hence 
they are not real natural poems. Origen, the Neo-Platonist, 
according to the witness of Porphyry,’ wrote only two works: 
περὶ δαιμόιων and ὅτι μόνος ποιητὴς ὁ βασιλεύς. Origen the 


2 Anal. Post. i. 14. 
4 Phys. i. 4. 


1 thie. Nicom. ii. 4. 
3 De Coelo, iil. ὃ. 
5 Vit. Plot. c. iii.; ef. ibid. c. xx. 


Cesare, Camestres, Festino, Baroco 417 
4 


nS 





Theologi 1 
gıan has written many other works, which Porphvr 
knew of, so that the assertion cannot be true of hi h ord 
ai | rue of him that he 
: : a na 
en these and only these writings. Hence Origen the Theo 
ogian W 1 N a the ; 
gian was not Origen the Neo-Platonist. On the other hand 
nothing would follow fr a: The 
: ms w from the two affirmative premises: The 
Neo-Pl: as | 
εν! ıtonist Origen was (according to Porphyry) a scholar 
4 , : z - - 3 < q « x 
— Saccas: The theologian of the same name was! 
a scholar S | ic 
a = ar of Ammonius Saccas. The astronomer Leverrier 
cone : 
uded: The sum total of the worlds belonging to our solar 
sys i ‘of | th 
: stem must completely determine the orbit of Uranus: the 
ΠΟΥ wor * solar sy | 
k cosa of our solar system do not fully account for the 
or : 
it 0 seca : Hence the whole of them are not known—a 
negativ "hi | | 
8 tive knowledge which prepared the way for the positive 
discover cl 1 
= ery of the existence, place, and size of Neptune 
estino.— ‘ealisati 
Β΄... ne realisation of a blind (thought of as determined 
pe g ‘ the method of Epicurus, and not originally by end 
anc physical causality and chemical force of nature does 
not lead to organisms i ious i 
N Ἑ 18 ingeniously articulated and reproducing 
selves. Some processes of nature lead to such organisms 
Hence (at least) s poner 
ome natural processes are not a realisation of 
a = - Ξ . . - ζῇ 
> poseless physical causality and chemical natural force 
aroco,— i rer is tr th it 
5... " Whatever is true must thoroughly agree with itself 
and w - ' 
= 1 undoubted facts. Some theorems of the Kantian sys 
en or 7 ACT 1 canal 
; do Ps thoroughly agree with themselves nor with undoubted 
acts. 
ence (at least) some theorems of the Kantian system 
are n 
we ot true. All regular plane figures (in the strictest sense 
if this RE: se 
1s notion) may be inscribed within a circle. Some parallelo 
oran γα ¢ . ὲ ae . . . ‘ 5 
E cannot be inscribed within a circle. Therefore some 
rar: t ig | 
para ams are not regular plane figures. All who are 
morally di is ΤΊ ' i | 
Ἢ y disposed do what is right with right intention. Some 
rho ; 1 | 
act in accordance with law, do not do what is richt wi h 
right intention. Therefor a 
g ; erefore, some who act legally are not morall 
disposed. i sists 
TI . 
1e w i 
ways in which the Schoolmen, following Aristotl 
reduce the moods of the 5 i a 
16 Second, Third, and Fourth Ficures to 
gures 


1 Acc i ἢ . ᾽ : 
ording to Porphyry in Euseb. Church History, vi. 19, 3. 
E E 














418 § 113. Vald Moods of the Second Figure— 





the corresponding mood of the First, is denoted in their names 
by the consonants 8, P, M, and Ο. 


s conversio simplex, 

p conversio per accidens sive in particul. propositionem, 

m Metathesis praemissarum, 

C conversio syllogismi,' or ductio per Contradietoriam pro- 

positionem sive per impossibile. 

Accordingly, in Cesare (where the 8 is to be regarded as the 
consonant of inference in the first syllable) the first or major 
premise is changed by conversio simplex from P e M to MeP, 
and the inference becomes Celarent :— . 

Me P 

S a M 

S eo P 
This reduction is of course perfectly capable of proof, and as 
little to be found fault with in itself as the demonstration of a 
mathematical theorem which is deduced from an earlier theorem 
by means of an auxiliary proposition, for the procedure does 
not destroy its authority to be considered as a new and peculiar 
theorem. But since proof may be led by means of a compari- 
son of spheres without reduction, and a stronger conviction 
reached by sensible representation, the direct way is to be pre- 
ferred. In the comparison of spheres there lies a general 
principle, which makes it possible to test immediately in each 
given case whether a valid conclusion results and what figure 
it must take, without first requiring a special recollection of 
the figure and mood. 

The like holds good and true of the other Reductions. 

In Camestres there must be a change of the internal relation 
of premises, by which the major premise becomes the minor, 
and vice versa (which is symbolically denoted by the external 
change of place), then the negative premise is converted 
simply, and last, the conclusion is simply converted. Thus: 


Ps 3 
Se M 


1 According to Aristotle, Top. vill. 14, 163 4, 32: ἀντιστρέφειν. 


demonstration is applied. 
premises : 


Cesare, Camestres, Festino, Baroco 





becomes first : 


then : 
5 
a M 
from which, according to Celarent in the First Figure follows : 
res 
from which, lastly, by conversio simplex, comes: 
> u 8 


I . . 

Βοίων - oe modern logicians (as for example 
ed another, by the Contrapositi 

‘ position of the maj 

be ajor pre- 

= Eee is Er preferred because it does away a 
n of the minor premise, which i | 
ıs unnatural in 

cases. It is, however, inferior i pete 

| orin v ; N 
i ν ; value to the direct comparison 


In Festi 1 
no ] i 
‚as in Cesare, the major premise only is converted 
ι > 


and the conclusion is drawn in Ferio 


In B ey 
aroco the ductio per impossibile or the apagogical 
3 Ἐν 
In order to prove that from the 


the conclusion : 


ἌΡΗΟΣ follows, it is shown that the contradictory opposit 
. . ᾿ 5 

Se re viz. 8 a P, could not co-exist with Fr pre- 

er Ἢ arti As = is thought along with the major premise 

5 ollows in the First Fi i 

; ae t gure according to Bar- 
= which is the contradictory opposite of the pele ack 

premise, and therefore must be as false as S 9 M is true 


Hence the admissio 1 
ssion which led to this fal 
ie ne gerri s false result must also be 


Hence the contradictory 


1 Log. § 384; cf. $ 399. 


: 2 








meant 

















δ 114. The 1) hird Figure, etc. 


S o P must.be true; which was to be proved. This 
to be. 


so unnatural as it at first may appear 
If (according to Trendelenburg) thought at first sight deduces 
from the given judgments: all squares are parallelograms : 
some regular rectilineal figures are not parallelograms, the 
inference: some regular rectilineal figures are not squares 
analysis might discover in this process of thought the implied 
hidden reflective consciousness, which, only slightly modified, 
is brought to the light of consciousness by the Aristotelian- 
Scholastic Reduction :—for if they were squares they would 
be parallelograms, which they are not. This Reduction is at 
least as natural as the Wolffian, by the Ὁ ontraposition of the 


420 


opposite 
Reduction is not 


ample: What is. not a paral- 


major premise—e.g. in that ex 
lelogram is not a square. 
Baroco may also be refe 


Cesare, when those (some) S of 
true be placed under a special notion and denoted by S|, 


Then the conclusion must hold good universally of S! and 
Ξ J ’ 


consequently particularly of ὃ. Aristotle calls such a pro- 
Cf. § 115. Demonstration of every kind of 


mmediate comparison of spheres is to be pre- 
s upon Reduction, ef. App. A.] 


rred to Camestres and Festino to 
which the minor premise 19 


cedure ἔκθεσι." 


reduction by the 1 
ferred. [For Hamilton’s view 


$ 114. In the Third Figure, whose general scheme 


is the following (ὃ 103)— 
M 


P 
the minor premise must be affirmative. For if it is nega- 
tive(MeSorMo S) where, according to the general 
rules (§§ 106-108 ), the major premise must be universally 
affirmative (M a P), then it remains uncertain whether 
the S, which (in M e S) is thought to be separated from 


1 Arist. Anal. Pri. i. 6. 


S 2: 
δ 115. Valıd Moods of the Third Figure, etc. 421 





the whole sphere of M, or at least (in M o S) ἢ 
part of that sphere, may perhaps fall within wi 
part of the sphere of P (perhaps as a ER - 
ordinate with M under the genus P), whether it 5 a 
= age > " or whether it lies ‘halite bee go 
sp rere. and P were understo 
indifferent signs of the two Ei ce = 
and inMo S, an inference of the form P S zZ x = 
would result. But then, in reference t a ; s 
oe yan o this conclusion, 
| 9 6 premise is no longer the minor but the 
major premise. For the S has become the major noti 
the praedicatum conclusionis, and the el ἐμ: = 
tive premise is the minor premise. It a in the 


moods Zelapton and Bocardo. ) 


ΠῚ lil , 
16 forms of combination which are rejected by this are: 
ae and ao 


Hen inati 
ce of the eight combinations whose validity stands the test 


of the general rules 12° 
5 al rules (§§ 106— ; 2 
Re ($$ 106-108), the following six remain 


nust c V < De 


N 115 r . 
#22: τ | , 7 , 
πο ἊΡ valid moods of the Third Figure have the 
Saal, eao,1ai, aii, oa rm 
the names Darapti, F Be Ihey take 
ap ıwraptı, Felapton, Disamis, Datisi, Bocard 
Ferison. The vowels i FRE EET GY, 
ve πὰ vowels in them denote in succession the 
"mo δῶν, . ‘i 
pee εἰ, e major and minor premises and the conclu- 
“oe = 168 consonants refer to the Aristotelian-Scholastic 
ction. 6 als icy 
Bere : Here also the proof of the validity results 
immediate comparison of spheres Ϊ 
) 5. 








422 § 115. Valid Moods of the Third Figure— 








The general scheme of the Third Figure— 


M ᾽ν 
M > 


S P 
takes in the mood Darapti the more definite form: 


us Ὁ 
Mas 


ΒΞ ΕΣ 








According to the premises the sphere of M is a common 
part of the spheres of P and S. Hence these latter 
must also coincide with each other in this part ; while 
the relation of their other parts, if there be any, remains 
‘ndefinite. Hence the conclusion holds good: At 
least one part of the sphere of S belongs to the pre- 
dicate P. 

In every example where both extremes may be made 
substantive, a double inference may be deduced from the 


same premises; e.g. when these terms are A and B, 
But since in both cases the 


AiB as well as BIA. 
of a universal affirmative 


major premise in each is 
form, and the same thing is done with the minor premise 


in each, there result, as has been remarked above (ὃ 113), 
two different examples of the same syllogistic mood, 
not, as in Cesare and Camestres, two different moods. 


The mood Felapton has the form— 


Mer 
Mas 


u Ὁ 





Darapti, Felapton, Disamis, Datisi, etc. 423 





The proof of its validity lies in this, that those S with 
which με coincides must together with M itself be 
separated from P. | 

“ὙΠ Hence (at least) some S are 


The form of the mood Disamis is the following :— 
Ἐ ΤΥ 
Mas 
ee 
If the spheres of M and P are partially united, and if 
M falls wholly within S, then S must also be sartiall 
united with P, viz. in that part at least with ke = 
portion of M falling within P coincides. (If only s 
M are P and others not, all S cannot be P, but in an 
case also only some S are P; cf. under Pine ) : 
The mood Datisi is of a wholly similar kind Th 
ΟΟΘΘΜΗΒΔΌ is made from the same premises as in Divası " 
The proposition which is the converse of the Be 
of Disamis is taken as the conclusion. The aaa 
proposition which there was major premise is here ie 


minor; and the universal proposition is the major pre 
mise. The form of this mood is— 


= @ F 

= δ. 

> ἤει 
Those ὃ with which a part of M coincides, because this 
part along with the whole sphere of M falls within the 
sphere of P, must be included with it in this same sphere 


Hence at least some S must have the predicate P. (If 
only some M are S, all S may yet be P.) 

















. 424 §115. Valid Moods of the Third Figure— 








The mood Bocardo has the form— 


“Mo? 
Ma 9 


5" We; 


If some M are not P, and all M are S, then any one 
part of the sphere of δ co-exists (according to the minor 
premise) with every part of M, and, consequently, with 
that part which (according to the major premise) 1s 
separated from P. Hence a part of the sphere of S is 
separated from the sphere of P, i.e. one or some S are 
not P. (It may happen that those S which do not 
coincide with M are separated from P; on the other 
hand, even ‘if no M is P, still some S may be P. But 
if only some M are not P, and others are, it 1s impossible 
that no ὃ are P. In this case if only some 5 are not F, 
others are always P, according to Disamis.) 
Ferison, lastly, has the following form :— 


MeP 
ἊΣ Ὁ 5 


So P 





% 





Those S at least with which a part of M coincides must 
with it be separated from P, because this part along 
with the whole of M is separated from P. Hence it 
remains uncertain whether the sphere of S has also 
parts which he without M, and, if it has, what relation 
they have to P. Therefore perhaps all, and at least 
some, S are not P. (If only some M are S, and also 


1 all M are S, the case may occur in which some > 
P and others are not; but the case may also occur in 


are 


Daraptı, Felapton, Disamis, Datisi, ete. 425 





which all S are not P. Itis always certain, however 
that at least some S are not P.) 


Exam .- 
: ples to Darapti. All whales are mammalia Ἢ all 
W E es are water anımals . Hence some water anımals are a 
maila. . 1 
Or All cetaceous animals are water animals ; all 
9 


cetaceous animals are mammalia: Hence some mammalia ar 


water animals, e 


ki ; The verb ıubeo takes the construction of the 
ΜΝ A an infinitive ; the verb iubeo is a verb which has 
0 ὡς m what is to be (not with what is): Hence at least a 
er ο i oe which have to do with what is to be (and not 
with what is) take the con | 
struction of the i 1 
= accusative and in- 
i ve. / ice singular judgment is to be considered as an 
I = . . h 
universal, because the subject is a definite individual. ΟἹ 
70.) © 
To F. —_ 1 
5... ne Iubeo is not a verb sentiendi vel declarandi : 
. )eo takes the. construction of the accusative and en. 
enc 1 | 
ΣΝ αἱ ἫΝ one or some Latin verbs which take the con 
‘uction of accusative and infiniti : 
nitive are no iendi 
wre) Picken t verbs sentiendi 
ἐὺ; . . 
O BE 
Bi. ag Some pronouns of the French language take 
᾿ nilection ; all French pronouns are words of the Trek 
language: Hence some words in the French language tak 
inflection. ae are ee 
ἐὴ . . τον . . 
᾿ 0 Datisi.—All inferences in Darapti belong to one and the 
sam . 1 1 
" e mood; some inferences in Darapti are inferences from 
e N . . . ΓῚ 
= = premises with conclusions which are the converse of 
ach other: 1 
pe other: Hence some inferences from the same premises 
7] . . 4 
| conclusions which are the converse of each other, bel 
to one and the same mood. All inferences, the f Ber 
Ne 3 one of which 
= rigen in Cesare and the other in Camestres (and also 
se ın Disamis and Dati 1) 
si), belong to two diff 
ifferent moods: 
some is ki We 
> inferences of this kind are inferences from the same 2 
uses, Ww 1 | : 
2 es, wıth conclusions the converse of each other: Hence some 
nferences fr 1 1 
= < from es παρῇ premises, with conclusions which 
ἕ onverse of eac 1 
Kran: : other, belong to two different moods. 
a >. 0.—Dome persons accused of witchcraft have not 
emselves to be free from the guilt laid to their 








ar 


. 


— 
— . - a 
- -— e x é 


Hoe ia er 


— 


Che a ar θύγὰν 


>. a 


ἜΣ Ve mad 


a 
τος δι τος 


sum 





426 § 115. Valid Moods of the Third Figure, ete. 





charge; all those accused of witchcraft were accused of a 
merely feigned crime: Hence some who were accused of a 
merely feigned crime have not believed themselves free from 
the guilt laid to their charge. 

To Ferison.—No syllogistic mood can be passed over in a 
scientific syllogistic; some syllogistic moods are moods which 
are inferior in scientific value to the principal moods of the 
First and Second Figures: Hence (at least) some moods which 
are inferior in scientific value to the principal moods of the First 
and Second Figures cannot be passed over in a scientific syllo- 
gistic. 

The Aristotelian-Scholastic method: of Reduction is here 
also denoted in the name of the mood. 

In Darapti, the D and the p denote: By conversion of the 
universal affirmative minor premise M a § into the particular 
affirmative Si M, the mood Darii of the First Figure results, 
which gives the sought-for conclusion SiP. 

In like manner Felapton is reduced by the conversio Par- 
ticularis of the minor premise to Ferio. | 

In Disamis the minor premise cannot be converted, for then 
there would be two particular premises. Hence the (particular 
affirmative) is converted simply, and the premises transposed, 
and there now results an inference in Dari not of the form 
S P but of the form P S. It is an inference of the kind 
that the proposition originally given as major premise serves 
rather as minor premise, and that given as minor premise as 
major, and a Metathesis praemissarum is the necessary (a re- 

ciprocal change of the internal relation of the premises, 
whether the external position, which is the symbol of this 
relation, is changed or not). Lastly, by a conversio Simplex 
of the conclusion, the conclusion proper to this mood is 
reached. 

Reduction is easier in Datisi, where only the conversio 
simplex of the minor premise is needed in order that the in- 
ference according to Darii may take directly its own proper 


form. 
All these moods, as Aristotle has correctly remarked,’ may 


1 Anal. Pri. i. c. vi. 


§ 116. The Fourth Figure, ete. 427 





also be shown to be valid indirectly or apagogically. Disamis 
and Datisi may also be reduced to Darapti by ἔκθεσις, i.e. Ὁ 
exclusion of a part; in Disamis those (some) M Been a Ρ, 
and in Datisi those M which are S, are excluded from the aie 
total of all M, and placed under a special notion, and accord- 
ingly denoted by a special letter, say N. Now since what was 
true of all M must be true of these N, N may be placed 
instead of M in the other premise, so that in both moods the 
premises take the form: Na P; NaS: from which, ac- 
cording to Darapti, follows S i P. 
The validity of the mood Bocardo is apagogically proved (as 
the validity of Baroco in the Second Figure wes) by Related 
and the Schoolmen. If the proposition were false, that some 
S are not P, and if its contradictory opposite were true that 
all S are P, then when we think this proposition and the given 
minor premise, according to which all M are S, it follows in 
Barbara, in the First Figure, that all M are P. This con- 
tradicts the given major premise which asserts that some M are 
not P. Hence the proposition which led to this contradiction 
cannot be true, viz. that all S are P. Hence some S are not 
P; which was to be proved. Aristotle remarks, that this 
mood may be proved without apagogical procedure, by the 
ἐκθέσθαι or λαμβάνειν of that part of the middle notion which 
is true of the major premise. If we denote this part by N, then 
(as above) we get the premises: Ne P; NaS: ‘mm 
which follows in Felapton S 0 P; which was to be proved. 
The mood Ferison, lastly, as the characteristic letters F and 
8 show, is reduced by conversio simplex of the minor premise 
to Ferio, according to which form M e P and S i M follows 
ΟΡ; which was to be proved. This mood may also be 


reduced to Felapton by ἔκθεσι». 
$ 116. The Fourth Figure (or second division of the 


First Figure in the wider sense), whose general scheme 
(§ 103) is the following :— 











428 


§ 116. The Fourth Figure, ete. 





cannot have a particular negative premise. The com- 
bination of a universal affirmative major premise with 
a particular affirmative minor is also excluded. For if 
a premise is particular negative, the other premise 
must be universal affirmative, according to the general 
rules (§§ 106-108); so that the two forms result— 


1, aa τ΄ ΣΝ 2. PaM 
Mas M' o 8 


But (according to 1), P is particularly \separated from 
M, and M falls wholly within S. Hence it is uncertain 
what relation M, thought as subject, has to P, when P 
is thought as predicate; for the particular negative 
judgment’ does not admit of conversion\(§ 88). Now 
it remains uncertain (according to the minor premise) 
whether, and how far, the sphere of S projects beyond 
that of M, and, therefore, the relation between S and P 
is quite indistinct, and no decision can be come to about 
the relation of Sto P. (If the meaning of the premise 
P o M were that only some P are not M and others are, 
then from the judgment P i M thought implicitly along 
with Ma 9 a definite conclusion Si P in the mood 
Dimatis would result; but this is not the sense of the 
particular judgment.) 

If (according to 2) M is particularly separated from 
S, but wholly includes the sphere of P, the relation of 
P to Sand of 8 to P remains quite indeterminate. For 
P may quite as well fall within the part of M separated 
from S, as either wholly or partly in the part of M which 
may coincide with S, and this again either so that 5 falls 
wholly or partly within P. (This relation would remain 


§117. Vahd Moods of the Fourth Figure, etc. 429 








indefinite even if the sense of MoS were: only some 
M are not ὃ. See below.) 


In the combination a i— 
r « & 
= £ 8 


in which P falls wholly within M, and M partly within 
S, it remains undetermined which part of M falls within 
S, whether it is a part which coincides with P or with 
a part of P, or only a part that lies outside of P. Hence 
the relation between S and P remains quite undeter- 
mined. (This relation would also remain indeterminate 
if the meaning of M i S were: Only some M are S, and 
others not. See above.) | 


Since accordingly the forms of combination : 


oa 20 ai 


are rejected, there remain for the Fourth Figure of the eicht 
combinations warranted by the general rules (§§ 106-8) the 
following five which lead to valid inferences :— 


aa ae ia ea ei 


$ 117. The valid moods of the Fourth Figure (or of 
the second division of the First F' ıgure in the wider sense) 
have the forms aai aee iai eao eio. They 
take | the names Bamalip, Calemes, Dimatis, Fesapo, 
Fresison. In these the vowels in their succession denote 
the form of the major and minor premises and Con- 
clusion, and the consonants refer to the Aristotelian- 
Scholastic Reduction. The ground of validity lies here 
also in the relation of spheres, and proof may be given 
by a direct comparison of spheres. 





430 $ 117. Valid Moods of the Fourth Figure, etc.— 





The universal scheme of the Fourth Figure— 





takes in the mood Bamalip the more definite form— 


Ῥ» ἃ 

Mas 

> τ 
According to the premises the terms have here the same 
relation to each other as in the mood Barbara of the First 
Figure, only P and S exchange characters ; the sphere 
of P falls’ wholly within the sphere of M, which is 
either identical with it or more extended, and this again 
wholly within the sphere of 5, either identical with it 
or more extended. The judgment P aS follows at 
once from this relation of spheres, and just as directly 
follows the judgment Si P. In the case of the identity 
of all three spheres all S are P, in all other cases only 
some Sare P. If this case does exist in a given example, 
it cannot be decided that it does so from the given pre- 
mises unless something further is given. But nothing 
further is required to attain with certainty the conclusion 
S i P, in the sense: At least some S are P; which was 


to be proved. 
The mood Calemes has the form— 


Ps 4 
Mes 


S ἃ ΣΦ 








Bamahp, Calemes, Dimatis, Fesapo, Fresison. 431 





The relation of terms is here the same as in Celarent, in 
the First Figure, only that P and S again exchange the 
parts they have to play. There is required here, as 
little as in Bamalip, a Conversion of the conclusion Pe ὃ 
which results according to the First Figure, in order 
to reach Se P. The judgment: S is wholly separated 
from P, or: No S is P, may be established directly on 
the relation of spheres, according to which M and S are 
wholly separated from each other, while P lies wholly 
within M. 


The mood Dimatis has the following scheme :— 


a, * m 
ms 6 


as & 





The relation of the spheres is the same as in Darii, 
when the extremes exchange places: M coincides in 
its whole extent with S or with a part of S, and at 
least in part of its extent with part of the extent of 
P. Hence it follows that Sand P must coincide with 
each other, at least particularly, in that part, namely, 
which they both have in common with M. Conse- 
quently, at least some S are P; which was to be proved. 
(If only some P, as well as if all, P are M, the case may 
occur that only some S are P, and also the other, that 


all S are P.) 
The form of the mood Fesapo is— 


r «* 2 
ym ἃ 8 


π΄ a Ὁ 














432 ὃ 117. Valid Moods of the Fourth figure, ete.— 





According to the premises, P and M are quite separated 
from each other, while M falls wholly within 8. Hence 
those S at least which coincide with M must also be 
separated from P: At least some S are not P. No 
corresponding mood exists in the First Figure in the 
stricter sense, because from the given premises nothing 
definite can be obtained about the relation of P to S. 
The sphere of S may project itself over that of M in 
such a way that at the same time all P, or that some P, 
may fall within it; but it may be so limited that it 
remains quite separate from P and P quite separate 


from it. 
The mood Fresison, lastly, has the following form :— 


P eM 
a 8 


> © £ 
This mood is distinguished from Fesapo by the par- 





ticular character of the minor premise. Those S which 
coineide with part of M, because this part along with 
the whole of M is separated from P, must be separated 
from P. Hence at least some S are not P. (When 
only some M, as well as when all M, are S, the case may 
occur that only some S’are not P, and.also the other 
case, that all S are not P, or that no Sis P.) Here 
also as in Fesapo the sphere of P may have every con- 
ceivable relation to that of S; and for this reason, no 
analogous mood can exist in the First Figure in the 


strieter sense. 


Inferences from the same premises, from which inferences in 
Barbara, Celerent, and Darii may be constructed, may serve as 


Bamalip, Calemes, Dimatis, Fresapo, Fresison. 433 








examples to Bamalip, Calemes, and Dimatis, where each of 
the two extremes may naturally take the place of the subject 
as well as that of the predicate. From the premises: Good non- 
conductors of heat retain heat longer ; woollen clothes are eood 
non-conductors—itis concluded in Barbara of the First art 

Therefore woollen clothes retain heat longer. If we first think 
of the end of preserving warmth, and if we then seek for means 
to attain to this end, we advance naturally from the same pre- 
mises to the conclusion in the form of the mood Bamalip : 
Some things which retain heat longer (some of the means ω 
retain heat longer) are woollen clothes. From the premises : 
All squares are parallelograms ; no parallelogram has converg- 
ing opposite sides—the conclusion is naturally drawn, ον δεν 
to Celarent, and not according to Calemes, because the wail 
cate—having converging sides—does not properly take the 
form of a substantive predicate-notion. But if the second pre- 
mise is: No parallelogram is a trapezoid, both inferences are 
equally natural: No square is a trapezoid, and: No trapezoid 
is a square. From the premises: Some parallelograms are 
squares; all squares are regular figures—follows, berlin to 
Dimatis : Some regular figures are parallelograms, and sccord- 
ing to Darii: Some parallelograms are regular figures. 

N o mood in the Fourth Figure corresponds ts Perio in the 
First, which is based on the particular negative form of the 
conclusion, nor on the other hand the moods Fesapo and Fre- 
sison find correlates in the First. 

; The following is an inference in F esapo. None of those 
inferences which fall under the definition enunciated by Ari- 
stotle! of inferences in the First Figure is a conclusion of the 
form Fesapo (nor of the form F resison) ; every inference of the 
form Fesapo (and of the form Fresison) is an inference of the 
Fourth Figure ; consequently, (at least) some inferences of the 
F ourth Figure do not fall under Aristotle’s definition of infer- 
ences in the First Figure. (It cannot be determined from the 
given premises only, without reference to other data, whether 
only some do not, or perhaps all do not; yet the result inferred 


1 Anal. Pr. i. 32. 
F F 


RR ee: Print” 


Ze were 


ve yah RT 
- ee > 





434 ἢ 117. Valid Moods of the Fourth Figure, οὐ 











from that has a distinct scientific value in and for itself. nl 
an essential moment in the explanation of the ee 0 > 
Aristotelian syllogistic to the later doctrine of Er = ee 
gistic figures.) In the foregoing example, if —n Ina 
moods themselves the attribute is given whic P = 
them falling under that definition, an -_—_ τ er 
Fresison occurs. None of those inferences which fa un . a 
Aristotelian definition of the First Figure has a acer aad 
mise in which the middle notion is the predicate : ΝΗ Ἔν 
with a negative premise in which the middle notion is ea : 
are inferences of the Fourth Figure : Therefore veges + 
(at least) of the Fourth Figure do not fall under the Arıs 
Ι finition of the First. | 
grt logicians proved the validity of sees mess eo 
had done the validity of the moods of the spree a 
Figures, by Reduction to the moods of the First Figur 
1 nse. . 
a Bamalip, the conclusion P a S in ea " 
first drawn by the reciprocal change of παν . net 
the premises symbolised by that (m) of ee na Pe» 
and then this conclusion is converted by conversio per : 8 
sive in particularem propositionem (P) to SIP. BR 
In Calemes, the conclusion P e ὼ is first formed, τῷ eon ; 
to Celarent, with metathesis praemissarum (m), and then 18 
changed to S e P by conversio simplex (8). EEE 
In like manner Dimatis is reduced to Dariz, anc 
ion si > converted. 
τ προς ee to Ferio by conversio simplex (8) of sg 
universal negative) major premise, and the conversio in partic. 
propos. (p) of the (universal affirmative) was gener ba 
Fresison is converted to Ferio by a conversio simplex ( 
jor and minor premises. | 
ge Scholastic Teiche who, following ——— 
reckon the five moods under consideration as indirect u. 
of the First Figure, consider the subject of the conclusion ar 
these moods to be the major extreme or the ee. νην 
the predicate of the conclusion the minor. They designate ὃ 





§ 118. The Different Figures and Moods, etc. 4 3 











arrange the premises in a corresponding manner. Those 
logicians give the following names: Baralip (or Baralipton), 
Celantes, Dabitis, Fapesmo, Friseson (or F risesomorum). In 
this mode of designation there undeniably lies an inconsequence 
because the general principle of distinguishing the major and 
minor notion, and accordingly the major and minor premise, 
according to the form of the conelusion, which has been 
followed in the designation of all other moods, is here aban- 
doned without reason. The mistake in the last two moods is 
especially striking. They cannot be caused or conceived by 
a conversion of a conclusion derived from the First Figure, and 
the relation of spheres of the terms in themselves, where they 
are not viewed in their position as subject and predicate in the 
premises, can as little justify the admission that here the S is 
the (higher) major notion, and P the (lower) minor notion. 


§ 118. From a comparative survey of the valid moods 
we find that the conclusion in all the figures— 

(a) can only be affirmative if both premises are affirma- 
tive (cf. Barbara, Darii; Darapti, Disamis, Datisi; Ba- 
malip, Dimatis) ; 

(b) must be negative if one premise is negative (cf. 
Celarent, Ferio; Cesare, Camestres, Festino, Baroco ; 
Felapton, Bocardo, Ferison; Calemes, Fesapo, Fresison) ; 

(c) is sometimes universal if both premises are uni- 
versal, viz. in the First and Second Figure, and in part 
of the Fourth (cf. Barbara, Celarent; Cesare, Camestres; 
Calemes); sometimes particular, viz. in the Third F igure 
and in part of the Fourth (cf. Darapti, F elapton; Ba- 
malip, Fesapo) ; 

(d) must be particular, if one premise is particular 
(cf. Darii, Ferio; Festino, Baroco ; Disamis, Datisi, 
Bocardo, Ferison; Dimatis, F resison). 

The First Figure admits conclusions of all forms 


rr2 


a ar 2 
R pier Ar 
Ce ree. Laat 


sien Zuge 


ΝΣ ΣῊΝ 





436 § 118. Comparative View of the 


(a, 6, i and o), the Second only negative (e and 0); the 
Third only particular (i and 0), the Fourth, particular 
affirmative, universal negative and particular negative 
conclusions (i, e and 0). 

A universal affirmative conclusion (a) can be deduced 
in the First Figure only (and in one mood only, Barbara) ; 
a universal negative (e) in the First, Second and Fourth 
Figures (in the four moods, Celarent; Cesare, Camestres; 
Calemes) ; a particular affirmative (i) in the First, Third 
and Fourth Figures only (in the ‘siz moods, Darn; 
Darapti, Disamis, Datisi; Bamalip, Dimatis); lastly, a 
particular negative (o) in all the figures (in the eight 
moods, Ferio; Festino, Baroco; Felapton, Bocardo, 
Ferison ; Fesapo, Fresison). 

The corresponding particular may be obtained from 
every universal conclusion by Subalternation. But in 
so far as the particular conclusions may be obtained 
immediately on the basis of premises by the comparison 
of the spheres, these modes of inference may be called 
Special moods. They take the names Barbari, Celaront; 

Cesaro, Camestros; Calemos. If these five moods are 
added to the previous ones, each of the four Figures has 
an equal number of six valid moods. But these new 
moods are meaningless, because only a part of what 
really results from the premises is taken. Besides 
the rules, given for the form of the conclusion ın 
general, remain valid when these moods are under con- 








sideration. | 
Universal affirmative conclusions have the highest 


scientific value, because they advance our knowledge 10 
a positive manner and admit of reliable application to 


Different Figures and Moods, ete. 437 





the individual. The universal negatives come next; 
they guarantee only a negative but a distinctly definite 
view. Then come the particular affirmatives, which 
promise a positive advance, but leave us helpless in the 
application to individual cases. Lastly, the particular 
negative conclusions are of the lowest value. Particular 
propositions, however, are by no means without scientific 
meaning. Their special service is to ward off false 
generalisations. The universal negative or affirmative 
judgment, falsely held to be true, is proved not true by 
the particular affirmative or negative conclusion, which 
is its contradictory opposite. 


Aristotle teaches,' that what is universal follows only from 
the universal, but sometimes something not universal follows 
from the universal, and either both or at least one premise 
must in reference to quality agree with the conclusion. Later 
logicians say : Conclusio sequitur partem debiliorem. This for- 
mula recommends itself by its apparent simplicity and clearness. 
It is not, however, minute nor distinct enough, but is incom- 
plete and apt to mislead. For if a, Θ; i, and Ο are successively 
‘weaker,’ i.e. are forms of successively lower scientific value, 
then, according to this rule, a conclusion from the premises of 
the forms & and e must necessarily come second as the pars 
debilior, and thus take the form e; but in Felapton and 
Fesapo it has the form 0, which is weaker still. Hence the 
rule must rather run: Conclusio non sequitur partem for- 
tiorem, sed aut sequitur partem debiliorem aut debiliore de- 
bilior est. If the meaning of the formula is more closely 
defined in this way, that the conclusion in reference to 
Quantity must be particular with a particular premise, and in 
reference to Quality negative with a negative premise, this 
definition is not false, only incomplete. For it is not said what 
form the conclusion may take, if both premises are either of 


1 Anal. Pri. i. 24. 








438 § 118. The Different Figures and Moods, etc. 





the same form (a &), or agree only in reference to Quantity 
(a e), or only in reference to Quality (a i). More particularly 
attention is not drawn to the different relations of Quantity 
and Quality, according to which both a and i, but not Θ nor 
0, can follow from a a, both Θ and O from & @, but not both i 
and o from 8 i. 

The versus memoriales (mnemonic verses) may be here in- 
serted. They contain the names of the whole of the moods of 
the Four Figures, and are not without value as an aid to the 


memory. 


Barbara, Celarent primae, Darii Ferioque. 

Cesare, Camestres, Festino, Baroco secundae. 
Tertia grande sonans recitat Darapti, Felapton, 
Disamis, Datisi, Bocardo, Ferison. Quartae 

Sunt Bamalip, Calemes, Dimatis, Fesapo, Fresison. 


The scholastic names of the moods were brought into common 
use by Petrus Hispanus (who died Pope John XXI. in the 
year 1277). He made use of them in his Compendium 
‘Summulae Logicales.’ (Prantl believes this to be a Latin 
translation from the work of Michael Psellus, who lived from 
1020-1106, Σύνοψες eis τὴν ᾿Αριστοτέλους λογικὴν ἐπιστήμην. 
The converse is rather true, as Thurot has proved ; the Σύνοψις 
is a translation of the Compendium of Petrus Hispanus. See 
above, $ 31.)' 

In Petrus Hispanus (and also in his predecessors William 
Shyreswood and others) the words run as follows: Barbara, 
Celarent, Darii, Ferio; Baralipton, Celantes, Dabitis, Fapesmo, 
Frisesomorum ; Cesare, Camestres, Festino, Baroco ; Darapti, 
Felapton, Disamis, Datisi, Bocardo, Ferison.2 The incon- 
sequence in the designation of the five Theophrastic moods 
induced later Latin logicians to change the names into Bamalip, 
Calemes, &c.2 The Greek reproduction of the Summulae 


ı ICH Prantl, ii. 275 ; Mansel’s edition of Aldrich’s Rudimenta, 4th 
ed. p. 84; Hamilton’s Diseussions, 2nd ed. p. 669. ] 

2 See Prantl, Gesch. d. Log. ii. 275; iii. 15 £. 

3 Cf. the remarks at § 117, p. 435. 


ra 


δ 119. Lhe Modality of the Syllogism. 439 





(Σύνοψις, &c.) has (according to the Augsburg MS. collated 
by Prantl) the following mnemonic words.'! For the four 
principal moods of the First Figure: γράμματα, ἔγραψε, 
γραφίδι, texvixos (which taken together have the meaning: 
Letters were written with the pen of a master) ; for the other Sve 
(Theophrastie} moods of this figure : γράμμασιν, ἔταξε, Χάρισι, 
πάρθενος, ἱερόν (by an inscription dedicated to the graces, a 
virgin, a temple); for the four moods of the Second Figure: 
ἔγραψε" κάτεχε μέτριον ἄχολον ; for the six moods of the Third 
Figure: ἅπασι σθεναρός, ἰσάκις ἀσπίδι ὁμαλός, φέριστος. Joh. 
Hospinianus, in a work upon the moods of the Categorical 
Syllogism,? enunciates the moods which are added by sub- 
alternation. Leibniz does so also in his De Arte Combina- 
toria,? and in his Nouv. Essais.* 


$ 119. If both premises are apodictic, or both proble- 
matic, the conclusion has a like Monatity, because the 
measure of its certainty is entirely dependent on the 
measure of the certainty of the premises. In all other 
respects the same rules hold good which are true of 
assertorical premises, because the relations of spheres 
are the same. 

If the modality of one premise differs from that of the 
other, the conclusion follows that which has the least 
certainty. For— 

(a) If the relation between the middle notion and 
the one term is of apodictic or assertorical certainty, and 
the relation between it and the other is problematic only, 

' They are copies of the Latin, but have not the signs of reduction. 
The same Greek words, with the exception of the names of the Theo- 
Phrastic moods, are also added, apparently by a later hand, to the 
Ἐπιτομὴ of Nicephorus Blemnides, published in 1250. 

2 Basel, 1560. 


* Erdmann’s edition of the Philosophical Works, pp. 13, 15. 
* Erdmann’s edition, p. 395. 


— Sy 


—-— 


ae ene - 
ee . ” ὟΣ J 





aorpeneran 


% . 
Fe 





r 2 
= Ξ ; = = 





440 §119. The Modality of the Syllogism. 





there exists co-ordinate with the last, and because of its 
problematic character, the opposite possibility. But 
this, when in combination with the unchanged (apodictic 
or assertoric) premise, does not lead by any form of 
combination to a conclusion absolutely the same, but in 
all cases excludes at least the certainty that the judg- 
ment contradictorily opposed to the conclusion is false. 
Hence the conclusion has only a problematic validity. 

(b) If one premise is of apodictic and the other of 
assertoric certainty, then the contradictory opposite of 
the latter is excluded only with assertoric not with 
apodictic certainty. Now this, connected with a pre- 
mise apodictically valid, would make it uncertain at 
least whether the judgment opposed to the conclusion 
as its contradictory be not true; and thus this uncer- 
tainty is excluded only assertorically, not apodictically, 
Hence the conclusion is true with assertorical certainty, 
not apodictically. 


Subjective uncertainty includes the consciousness that perhaps 
the opposite admission is true, and so real possibility as such is 
accompanied by the possibility of the opposite. Assertoric 
certainty excludes the opposite with assertoric certainty only, 
and the apodietie with apodictic certainty, and so actual exist- 
ence, in so far as it does.not prove itself to be founded on a 
universal conformability to law, excludes its opposite only as 
far as facts warrant, while necessary existence on the other 
hand necessarily excludes its opposite. Real relations must 
be mirrored in our consciousness, and so the knowledge of the 
real possibility or of the actual present capacity establishes a 
problematic judgment about its actual occurrence: which has 
to do with its possibility, and knowledge of the real necessity a 
corresponding apodictic judgment. But because it is not true 
conversely, that reality adapts itself to our knowledge, a real 


δ 119. Zhe Modality of the Syllogism. 441 





possibility does not always present itself where subjective 
uncertainty exists, and the real cause is not always to be 
recognised where a sufficient ground of knowledge makes strict 
demonstration possible, and therefore warrants apodictic cer- 
tainty. Accordingly, the cases where a problematic conclusion 
is obtained from problematic premises, in no way coincide with 
those where a judgment of possibility can be inferred from a 
judgment of possibility. Hence, for example, in the Second 
Figure from the premises: P is perhaps M; S is perhaps not 
M—the conclusion follows; S is perhaps not P. But from 
the premises: P has a possibility to be M; S has the possi- 
bility not to be M—the conclusion does not follow: S has the 
possibility not to be P. For the real possibility of a definite 
existence and of a corresponding non-existence is in itself the 
same, and therefore P and S have actually the same pre- 
dicate. And thus there are two affirmative premises in 
the Second Figure, from which, according to the universal 
rules of the Second Figure, nothing definite in the 
relation between S and P can be deduced. The judgments, 
however, in which any real possibility (or capacity) is adjudged 
to any subject are not necessarily problematic (which they 
become by a ‘ perhaps’ added in thought), but are in themselves 
assertoric (although the judgment originating from them upon 
the actual existence, which in them is thought as possible or 
exists in capacity, is problematic). Consequently the inferences 
formed from them fall under the general laws of conclusions 
from assertoric premises, and do not form a special form of 
inference, and so do not require a special representation. 
Aristotle} explains the manifold relations of forms of infer- 
ence which arise from the different modes of combination of 
the judgments of real possibility, real actual existence, and 
real necessity. He holds that under certain conditions, from 
the combination of a judgment of necessity with a judgment 
of actual existence, there results a judgment of necessity, and 
from a combination of a judgment of necessity with a judg- 


ment of possibility there results a judgment of actual ex- 
istence. | 
1 Anal. Pri. i. c. viil.—xxii. 

















442 § 120. Substitution of one Notion for another 








Theophrastus and Eudemus, however, teach that in these 
references the conclusion always follows the weaker premise. 
Alex. Aphrod. says:! οἱ δέ γε ἑταῖροι αὐτοῦ οἱ περὶ Ἐὔδημόν τε 
καὶ Θεόφραστον οὐχ οὕτως“ λέγουσιν, ἀλλά φασιν ἐν πάσαις ταῖς ἐξ 
ἀναγκαίας τε καὶ ὑπαρχούσης συζυγίαις, ἐὰν ὧσι κείμεναι συλλο- 
γιστικῶς, ὑπάρχον γίγνεσθαι τὸ συμπέρασμα. Philop. says :’ 
οἱ μέντοι περὶ Θεόφραστον καὶ ἐπὶ ταύτης τῆς συζυγίας (sc. τὸ A 
τῷ Β ἐξ ἀνάγκης οὐδενὶ ὑπάρχει, τὸ δὲ B ἐνδέχεται παντὶ τῷ I’) 
ἐνδεχόμενον λέγουσιν εἶναι τὸ συμπέρασμα (sc. τὸ A ἐνδέχεται τῷ 
Γ οὐδενὶ) ἵνα καὶ ἐνταῦθα τῇ χείρονι τῶν προτάσεων ἕπηται τὸ 
συμπέρασμα. Theophrastus and Eudemus are certainly correct 
here, for in syllogisms which refer to real relations of possi- 
bility, actuality, and necessity, every limitation which lies in 
one of the two premises passes over to the conclusion.? 


$ 120. It is not necessary to the validity of the in- 
ference that in both premises the relation of subject and 
premise should exist between the terms. The conclu- 
sion may also be formed, when for any one notion of the 
one premise (or fundamental judgment) which stands in 
an objective and attributive relation, another notion 15 SUB- 
STITUTED which is supplied by the second premise (or the 
auxiliary judgment). Instead of the sphere of the higher 
notion, taken universally, the sphere (or even part of 
the sphere) of a lower notion, which coincides with a 
part of the former, may be substituted, and in place (of 
the whole sphere or) of the indefinite part of the sphere 
of a lower notion, the indefinite part of the comprehend- 
ing sphere of a higher notion may be substituted. The 
form of the conclusion must strictly correspond to the 
form of that premise (or fundamental judgment) in 
which the new notion is substituted. 


1 Ad Anal. Pri. f. 49 A. 2 Ad eundem locum, f. 51 A. 
3 Cf. §§ 87, 98, and Prantl, Gesch. d. Logik, i. 278 ff., 370 ff. 


in an Objective or Attributive Relation, etc. 443 








The following inference may serve as an example, in which 
the notion for which another is substituted is EEE 
universally, and takes the place of the object in the funda- 
mental judgment: The earth attracts the whole of the bodies 
contained in its neighbourhood; the moon is a body existing 
in the neighbourhood of the earth: Hence the earth ne 
the moon. Or:! Love craves the beautiful; the Good is 
beautiful: Therefore Love craves the Good. In the following 
inference the attributive relation occurs: Abuse of the veceulations 
of those in authority deserves legal punishment ; the palltienl 
measures of the Government are regulations of those in autho- 
rity : Hence abuse of the political measures of the Government 
deserves legal punishment. In the following inference a 
higher notion is substituted for a notion taken partially in an 
attributive relation: The peculiar motion of (at least) some 
double stars is undoubted; all double stars are fixed stars: 
Hence the peculiar motion of some fixed stars is undoubted. | 

The inferences from two simple (containing only the predi- 
cative relation) categorical judgments may be placed under the 
same point of view, for the one may generally be considered as 
a fundamental judgment (in which the substitution is made) 
and the other as an auxiliary judgment (by means of which the 
substitution is made). According to $ 71, the subject is uni- 
versal in every universal judgment. Hence another subject- 
notion may be substituted for it whose sphere coincides with 
(at least) part of the sphere of the first subject. In every 
particular judgment the subject is particular, and so the in- 
definite part of another subject-notion, the sphere of which 
comprehends the sphere of the first subject, may be sub- 
stituted for it. The predicate in every affirmative judgment is 
particular, and hence a higher predicate-notion may be sub- 
stituted for it. Lastly, the predicate in every negative judg- 
ment is universal, and therefore a lower predicate-notion μων 
be substituted for it. This mode of consideration is less 
convenient in inferences of this kind because the distinction of 
both premises as fundamental and auxiliary judgment is not 


1 Plat. Sympos. c. xxi. 


























444 § 120. Substitution of one Notion for another 





thoroughly established in the nature of the case. In many 
cases also each of the two premises may be considered as the 
fundamental judgment, and each as the auxiliary judgment, 
and in a complete representation, according to this principle, a 
part of the moods must submit to a double construction. 
Hence the immediate comparison of spheres leads to the end 
in view in a simple and natural way. 

The Aristotelian-Scholastic Logic attempted a thorough 
explanation of inferences from simple categorical syllogisms 
only. The inferences, where a term is substituted by another 
in an attributive or objective relation, are left unnoticed. The 
first work which strictly takes up the question is the Logique 
ou l’Art de Penser, produced by the Cartesian School. It first 
- appeared in 1662, and its principal author was probably Ant. 
Arnauld. It calls syllogisms of this kind syllogismes complezes, 
and endeavours both to prove (only by examples, however) 
how they may be reduced to syllogismes incomplexes, and also 
to enunciate a principle according to which the force of infer- 
ence in all syllogisms may be at once estimated without 
reduction. The principle is: ‘that one of the two proposi- 
tions must contain the conclusion, and the other show that it 
contains it;’ the term of the conclusion substituted for it 
must be contained either in the extent or content of the 
middle term. The judgment which contains the conclusion 
may be called proposition contenante, and the one which proves 
that it is contained, applicative. In simple affirmative syllo- 
gisms each of the two premises may generally be conceived to 
be the contenante, because each in its way contains the con- 
clusion, and each is applicative. In negative syllogisms the 
negative premise is the contenante. In the syllogismes com- 
plexes it is the premise whose form determines the form of 
the conelusion.' The application of this principle to special 
cases would have led to a succession of special rules. But 
they are not developed in that logical treatise; individual 
examples only are analysed. 

Beneke has founded on this principle a complete theory of 


I Log. pt. ill. 6. 1X.—X1. 


in an Objective or Attributive Relation, etc. 445 





syllogism. He expounds this in his Logic.’ Beneke calls 
substitution the deepest fundamental relation in analytic in- 
ferences. In a given judgment (the fundamental judgment) 
we substitute for one of its elements another on the occasion 
of a second judgment (the auxiliary judgment), which shows 
the relation between the former and the new element. What 
is substituted may be a part of that for which it is substi- 
tuted, or the same thing conceived in a different way. It is 
a part when the extent of the term is divided. This case can 
only occur where the universal notion is true in the whole of 
its extent (‘ ambitum dividi posse, ubi totus adsit; non posse 
ubi non nisi pars eius inveniatur ’), i.e. in the subjects of every 
universal, and in the predicate of every negative judgment. 
It is the same in another apprehension when the content of a 
term is divided. This case can only occur when a notion is 
true in a part of its extent only (‘ complexus partem poni non 
posse, nisi quantitate data particulari’), because the part of 
the narrower sphere must also be a part of the wider in which 
the narrower lies; hence, in the subject of every particular 
and in the predicate of every affirmative judgment. 


‘Quod vero ad singulas formas attinet, in aperto est: 

in forma & ambitum subiecti et complexum prae- 
dicati, 

in forma @ ambitum subiecti et ambitum praedicati, 

in forma i complexum subiecti et complexum prae- 
dicati, 

in forma O denique complexum subiecti, et am- 
bitum praedicati partitionem admittere.’ 


Beneke’s exposition of syllogistic, according to this principle 
of substitution, is very valuable. The principle of the imme- 
diate comparison of the spheres of the three terms in simple 

1 Lehrbuch der Logik, p. 110 ff., 1832; in his Syllogismorum 
analyticorum origines et ordinem naturalem demonstravit Frid. Eduard. 
Beneke, Berol. 1839; and in his System der Logik, i. 201-245, 1842: 
cf. Dressler, Prakt. Denklehre, pp. 290-320, 1852; [and Prof. W. 
Stanley Jevons in his Substitution of Similars the true principle of 
Reasoning, Lond. 1869. | 





























446 § 121. The Syllogism from Subordinately Complex 








categorical syllogisms, according to which the relation of 
spheres between the two extremes may be directly sought on 
the basis of their relation to the middle-notion, without the 
fiction (‘alteram finge fundamentalem sive priorem, alteram 
accedentem sive posteriorem’) of a fundamental and auxiliary 
judgment, is to be preferred as the simpler and more nase 
The expressions, ‘ partition of extent, and ‘ partition of content, 
however, are inexact and misleading. In the so-called “ par- 
tition of extent’ a notion is indeed substituted whose sphere 
coincides with a part of the sphere of the former notion, and in 
the “ partition of content’ a notion, whose sphere partly coin- 
cides with the former notion, and which, therefore, if it belongs 
at all to its content in a special sense, belongs to part of it 
only; but that coincidence need not always denote a (partial) 
identity ; itmay also denote a connection. Cf. §§ 11, 85, 105. 

It appears ‘better to enunciate the rules belonging to the 
cases as we have done above, and thus avoid the expressions, 
‘ partition of extent ’ and ‘ partition of content,’ which are not 
appropriate in many and in the most important cases. Least 
of all can we agree to the consequence deduced by Beneke 
from that incorrect expression ‘ partition:’ ‘ syllogismos, qui 
per tot saecula numeris omnibus absoluti habiti sint, nihil 
ad scientiam humanam valere neque amplificandam neque 
provehendam.’ ‘What we gain is only division and clearness. 
This assertion is true of syllogisms formed from the Kantian 
‘analytic’ judgments, but false of syllogisms formed from syn- 
thetic judgments. Syllogisms of this latter kind, in so far as 
they rest on the foundation of real conformability to law, are 
the most essential means of extending and advancing human 
knowledge. Cf. § 101. 

Hamilton, like Beneke, but more definitely, founded the 
analysis of inferences on the ‘ quantification of the predicate.’ 
See above, $ 71 [ef. also Appendices A and B]. 


§ 121. All of the modes of inference which are found 


in categorical judgments are repeated in the subordinately 
c τι Fe 
complex, and especially in the HYPOTHETICAL Judgment. 


and especially from Hypothetical Premises. 447 





The proofs of their validity may be obtained in the 
same way by a comparison of spheres, provided that the 
coincidence and separation of spheres is made to signify 
not the relation of inherence, but the corresponding rela- 
tions of complex judgments, and more particularly the 
relation of dependence in hypothetical judgments. 


The thorough-going analogy of these relations with those 
of categorical inference, renders it unnecessary to do more 
than give individual examples of the different figures. 

The following is an hypothetical inference of the First 
Figure in the Mood Barbara (its minor precedes the major 
premise): If the earth is in motion, then the light of the fixed 
stars, so far as they do not lie in the (momentary) direction of 
the motion of the earth, must be perceived by means of another 
direction of the telescope and of the eye from that in which 
their position lies; If this is the case, the apparent position of 
the fixed stars, so far as they do not lie in the momentary 
direction of the movement of the earth, must be different from 
their true position. Hence, if the earth moves, the visible posi- 
tion of those stars must be different from their true position. 

The following inference belongs to the Second Figure and to 
the Mood Cesare (its minor premise is also placed first): If 
decided characters exist, then persons may be found who strive 
after great and noble ends, with real faithfulness and persist- 
ence. If the Kantian notion of transcendental freedom is true, 
no persons can be found who strive after such aims in such a 
manner. Hence, if decided characters exist, the Kantian 
notion of transcendental freedom has no truth. 

The following inference belongs to-the Third Figure and to 
the Mood Disamis: In certain cases, if a magnet approaches a 
non-electrified conductor, or recedes from it, an electric current 
originates in the latter. In all cases, whenever this experiment 
is made, magnetic powers only are directly called into opera- 
tion. Therefore, sometimes, when magnetic forces only are 
directly set in operation, an electric current is produced. 

A conclusion is made in the Fourth Figure and in the Mood 


























. 


448 δ 121. The Syllogism from Subordinately Complex 
Bamalip, if the premises of the example given above under the 
mood Barbara are not applied, as there, to explain the pheno- 
mena from the real cause, but in the opposite sense to get at 
the knowledge of the real cause from the actual phenomenon, or 
at least to pave the way for this knowledge. In some cases at 
least, and under certain presuppositions, if the apparent posi- 
tion of the stars, which do not lie in the (momentary ) direction 
of the earth, deviates from their true position, the earth moves. 
The particular form of the conclusion, which is necessary accord- 
ing to the general laws of this mood of inference, has not here 
the meaning, that sometimes (at certain times) only, the cause 
of the aberration of light lies in the motion of the earth, but 
denotes the uncertainty which attaches to the inference from 
the effect to the cause. It is only when the further proof has 
been given that the real cause received, which is sufiicient to ex- 
plain the phenomenon in consideration, is also the single reason 
possible, or the conditio sine qua non, that the problematical 
admission passes over into certain and universal knowledge. 
In the given example, the proof, that if the earth did not move, 
the aberration would not occur in the way that it does actually 
occur in astronomical observation, must also find a place. 
Aristotle does not recognise the scientific correctness of infer- 
ences, which he calls hypothetical (οἱ ἐξ ὑποθέσεως συλλογισμοί, 
in opposition to the δεικτικοὶ συλλογισμοί), because science does 
not result from inference from uncertain presuppositions (ὑπο- 
θέσεις), but only from inference from sure principles.' He 
understands by ὑπόθεσις a proposition conceded, which is 
neither proved nor is yet.immediately certain, and of which it 
τῷ affirmed that it either contains what is to be supposed to 
be true (διὰ συνθήκης ὡμολογημένον) and what is yet to be proved 
a truth or an untruth. The judgment passed by Aristotle 
may be justified in propositions of this kind, but does not 
at all concern hypothetical judgments in the later use of the 
phrase. For what is asserted of these in the premises and in 
the conclusion is not the actual existence of what conditions 








and what is conditioned, but the nexus or relation of dependence 


1 Anal. Pri. i. 44. 


and especially from Hypothetical Premises. 449 





between the conditioning and the conditioned. And this is not 
to be received as an arbitrary hypothesis, but as a scientific 
truth. It is an unquestionable fact, in spite of the contradic- 
tion of Waitz! and of Prantl,? that Aristotle did not formall 

comprehend under his notion of inferences ἐξ ὑποθέσεως, hy = 
thetical inferences in the later sense, and that his le 
therefore required this enlargement. He reckoned TE 
proof among the syllogisms hypothetical in his sense—roö 
δ᾽ ἐξ ὑποθέσεως μέρος τὸ διὰ τοῦ aduvarov’—because in it a 
false proposition, viz. the contradictory opposite of the pro- 
position to be proved, is hypothetically taken as true, in 
the meaning of the (real or feigned) opponent who might sali 
it, and so serves as an ὑπόθεσις, and forms the (δοὺς οὗ ἃ 
syllogism by means of which something evidently untrue is 
inferred,— because its contradictory is already recognised to 
be true, with the aim and in order to destroy the Salon hypo- 
thesis itself by showing the falsehood of its consequence. 

The remark of Aristotle : πολλοὶ δὲ καὶ ἕτεροι περαίνονται 
ἐξ ὑποθέσεως, ods ἐπισκέψασθαι δεῖ καὶ διασημῆναι καθαρῶς, a 
pears to have induced Theophrastus and Eudemus to eae 
struct more accurately the theory of hypothetical inference 

Boéthius says that, in the doctrine of the hypothetical s Πρ. 
gisms, ‘ Theophrastus rerum tantum summas exsequitur Bude- 
mus latiorem docendi graditur viam.’ Theophrastus tts in 
particular of the thoroughly hypothetical syllogisms, in which 
the premises are of the same form with sath δῶν and with 
the conclusion (οἱ δι’ ὅλου or δι’ ὅλων ὑποθετικοί, διὰ τριῶν ὑπο- 
θετικοί, called also by Theophrastus συλλογισμοὶ κατ᾽ dva- 
hoyiav), and have three syllogistic figures like categorical syllo- 
gisms. He appears to have made the hypothetical proposition 
(εἰ τὸ A, τὸ B) parallel with the categorical (τὸ A κατὰ 

τοῦ Β), the condition (εἰ τὸ A) with the predicate (τὸ A), and 

what is conditioned (τὸ B) with the subject (κατὰ τοῦ B) This 

at least is the only explanation of the fact® that he REF 


I Ad Arist. Org. i. 433. 2 Gesch. der Log. i. 272, 295. 


3 . ᾿ 
j aaa. Pri. 1. 28. 4 Ibid. i. 44. 5 De Syl. Hyp. p. 606. 
According to the accounts of Alex. Ad Anal. Pri. fol. 134: ef. 
Prantl, Gesch. der Log. i. 381. = 


GG 














450 § 121. Syllogism from Subordinateiy Complex, ete. 





that form of inference to be the Second Figure of the hypo- 
thetical syllogism, in which the premises beginning with the 
same condition end with a different conditioned: εἰ τὸ A, τὸ B- 
εἰ μὴ TOA, τὸ Γ΄ εἰ ἄρα μὴ τὸ B, τὸ I’; and that to be the 
Third Figure in which the premises beginning with a different 
condition and ending with the same conditioned: εἰ τὸ A, τὸ 
T'- εἰ τὸ B, οὐ τὸ Γ΄ εἰ dpa τὸ A, οὐ τὸ B. Theophrastus con- 
trives to find, by this way of paralleling, the most complete 
analogy between the First Figure of the Hypothetical inference 
and the First Figure of the Categorical, according to the fol- 
lowing position of the premises: εἰ τὸ A, τὸ B° εἰ τὸ B, τὸ I’: 
εἰ ἄρα τὸ Α, τὸ I. This opinion of Theophrastus may have 
determined his choice of the letters, since the early logicians, and 
Aristotle himself, made the letter which stood first in the 
alphabet denote the most general term, or what stands in 
the same relation as the general term. | 

But this way of paralleling the two kinds of inference is 
false. The condition is rather to be considered as analogous 
to the subject of the categorical proposition, and what is con- 
ditioned to the predicate. For the sphere of the cases in which 
the condition exists is not equal to the sphere of the predicate, 
which is the wider, but is equal to the sphere of the subject, 
which is either narrower or equal to the sphere of the con- 
ditioned. 

Alexander of Aphrodisias showed the true relation.’ He 
properly recognised the Third Figure in that hypothetical 
inference which Theophrastus made the Second, and the 
Second in that which he made the Third. 

The Stoics have paid special attention to hypothetical 
syllogism. 

Boéthius (in his writing De Syllogismo hypothetico) repre- 
sents the possible forms of conditional inferences with super- 
abundant detail. 

Kant refers hypothetical inference, as well as the hypothetical 
judgment, to the category of Dependence. R ὩΣ 

[ Hamilton, in his earlier writings, followed Kant’s opinion ; 


1 Ad Arist. Anal. Pri. fol. 134. 


§ 122. Mixed Inferences, ete. 451 





latterly he believed that all hypothetical inference could be 
classed under immediate inference." ] 

We agree with the opinion that the logical distinction between 
the categorical and hypothetical mode of inference rests on the 
metaphysical distinction between the categories of inherence and 
dependence. It is not to be considered, as some later logicians 
have done, only or almost only a difference in the verbal ex- 
pression. Cf. §§ 68, 85, and 94. 


§ 122. Mrxep INFERENCES are those whose premises are 
judgments which have different relations. HyPOTHETICO- 
CATEGORICAL inferences belong to this class. From the 
combination of an hypothetical premise with a categorical, 
which either asserts the fact of the condition or denies 


the fact of the conditioned, there follows in the first. 


case the categorical affirmation of what is conditioned 
(modus ponens), in the other case the categorical nega- 


tion of the condition (modus tollens). The modus. 


ponens corresponds to the First Figure of categorical 
inferences, the modus tollens to the Second. Different 
modifications, which correspond to the moods in the 
first two figures, result by the admission of negation 
into the second member of the hypothetical premise, 
as well as by that of the distinction of quantity (in 
some cases—in all cases). If the negation occurs in 
the first member of the hypothetical premise, the case 
corresponds to categorical inferences of the same 
figures which have a negative subject-notion in the 
major premise. No form of these inferences can 
agree with the Third and Fourth Figures of the cate- 
gorical syllogism (in whose minor premise the middle 


[! Cf. Lectures on Logic, ii. 376 ff. ] 
α62 


ar 


TP er en oo =~ 
ἄτας _ IT ἀπεις τς = ee eer ae ᾿ % x > RI Tr Ss EEE - = 
— no 3 Zr. ἊΝ - u ἊΝ - > en = “ = — RT = -- - » τῶν τὸ εἶ a om m μι 











δ 122. Mixed Inferences from an 


452 





notion is subject). For the condition in the hypo- 
thetical corresponds to the subject of the categorical 
judgments, and the subject does not occur in the minor 
premise where a categorical takes the place of a con- 


ditioned assertion. Hence in such an assertion the part 


mediating the inference would be wanting. 


The Scheme of the modus ponens, in the fundamental form 
which corresponds to the mood Barbara, and is more accurately 
called the modus ponendo ponens,! is: If A is, B is; A is: 
Therefore B is. Its formula was, as given by the older Logi- 
cians: posita conditione ponatur conditionatum. The modus 
ponendo tollens corresponds to the mood Celarent; If A is, B 
isnot; Ais: .*.Bis not. These moods pass over into Darii and 
Ferio, if the minor premise is: Sometimes or in some cases A 
is, and accordingly the conclusion is: ..B is in certain cases, 
and B is not in certain cases. If the major premise runs: If 
A is not, B is, or B is not; and the minor premise: A is not, 


the existence or non-existence of B foliows by a modus tollendo © 


ponens or tollendo tollens. The scheme of the modus tollens 
in its fundamental form, which corresponds to the mood Ca- 
mestres, and may more strictly be called modus tollendo tollens, 
is: If A is, Bis; now Bis not: .*. A is not. Its formula is as 
follows: sublato conditionato, tollatur conditio. The modus 
ponendo tollens corresponds to the mood Cesare: If A is, B is 
not; Β ἰδ: «᾽ν. Α isnot. The moods Baroco and Festino can in 
this case be formed in a way quite analogous to the construc- 
tion of Darii and Ferio. When the negation occurs in the 
first member of the hypothetical major premise, a modus tollendo 
ponens : If A is not, Bis; now Bis not: .΄. Ais; anda modus 
ponendo ponens: If A is not, B is not; now Bis: .*. A is— 
may be. formed. A conclusion from the conditioned to the 
condition is unjustifiable: If a is, Bis; now Bis: .*. Ais (Just as 
a categorical inference in the Second Figure from two affirma- 
tive premises is false); for the sphere of the cases where B is 
may be more extensive than the sphere of the case where A 1s, 


1 Drobisch, 3rd ed. § 98. 


Hypothetial and a Categorical Premise, etc. 453 





so that B can exist where Ais not. For the same reason the 
inference: If A is, Bis; now A is not: .". Bis not, is false (just 
as a categorical inference in the First Figure with a negative 
minor premise is not valid). 

In this case also, because of the thorough-going analogy, a few 
examples will suffice. Böckh! concludes, in opposition to 
Gruppe, in the modus ponendo ponens (and in the modus 
ponendo tollens) after the manner of the First Figure: If 
Plato in the Timaeus teaches the daily motion of the: heavens 
from the east to the west, he must deny the daily rotation of 
the earth on its axis from west to east (and so cannot teach the 
rotation of the earth on its axis); but he teaches the former: 
Therefore he must deny the latter (and cannot teach it). With 
equal correctness, Böckh, in the same book, in opposition to 
Stallbaum, argues in the modus tollendo tollens after the 
manner of the Second Figure: If Plato teaches the rotation of 
the earth about the axis of the universe, he must also accept 
the rotation of the earth round its own axis (for the one axis is 
only the lengthening of the other); but he denies the latter 
rotation: Therefore he denies the former also. 

Inferences of this kind, though only one of the premises is 
hypothetical and the other categorical, are commonly called 
hypothetical inferences, and so explained. The older Peripatetics 
(more particularly Theophrastus and Eudemus) have already 
made use of this opinion. ‘They call the hypothetical major 
premise τὸ συνημμένον, its conditioning member τὸ ἡγούμενον, 
the conditioned τὸ ἑπόμενον, the categorical minor premise 
μετάληψις, because it repeats categorically, or changes to this 
form, what was already asserted in the hypothetical major pre- 
mise as a member, and, lastly, the conclusion συμπέρασμα. 

The Stoics change the terminology without, as it appears, 
' They call the hypothetical 
major premise τὸ τροπικόν, or the major premise generally τὸ 
λῆμμα, its members τὸ ἡγούμενον and τὸ λῆγον, the categorical 
minor premise πρόσληψις, and, lastly, the conclusion, as in 
general, &mıdopa.? 


essentially advancing the doctrine. 


1 In his Untersuchungen über das Kosmische Systems des Plato, 1852. 
2 Cf. Philop. Ad Anal. Pr. fol. Ix. a. 


SRR GE AT Ree WN hE ν 














oS Se Se 


er tn ον σα 


— os — 
7 
nn nn nn 


ae 











454 § 122. Mixed Inferences, ete. 





Boéthius' gives a detailed enumeration of the forms here 
possible. 

Kant? holds that hypothetical inference of this kind is 
not properly ‘an inference of the reason,’ that is, is not a 
mediate but an immediate inference, because it has only two 
terms and no middle notion. In point of fact, however, it 
does not belong to the notion of immediate but to that of 
mediate inference, because the conclusion does not follow from 
one premise only, but from the combination of the two. The 
member which corresponds to the middle notion of categorical 
inference is not wanting; but what would correspond to the 
minor notion is absent. Hence the First and Second Figures 
find place, but not the Third nor Fourth. 

Reimarus, Herbart,‘ and Drobisch® have proved that these 
forms of inferences are parallel to the categorical. 

Herbart, however, incorrectly believes that he is able to 
enunciate a wholly analogous form of the catégorical inference 
in two terms: A is B; now Ais: «΄. Β is. For the categorical 


judgment, in distinction from the hypothetical, always includes 


the presupposition of the existence of the subject; and if the 
speaker asserts this in his own name, this existence, according 
to his own opinion, is presupposed; but if it is expressed in 
the sense of another, or in following up a circle of thought 
which proceeds upon an actual existence which is feigned, it is 
presupposed in this sense. Cf. above, $ 85. But if the mode 
of the existence of the subject is more closely defined in the 
minor premise (e.g. A has not a mythical but a real ex- 
istence) in order to vindicate for the predicate the same mode 
of existence in the conclusion; or if the present in the minor 
premise, and accordingly in the conclusion, has to do with the 
future of the person judging, more than two terms are present. 


The determination of the existence or of the time gives a 
third term. 


1 De Syllog. Hypoth. 614 sqq. 
3 Vernunftl. § 198. 
4 Lehrb. zur Einleit. in die Philos. $ 64 ff. 


2 Log. § 75. 


5 Log. §§ 94, 98. 


§ 123. Mixed Inferences with Co-ordinately, etc. 455 





§ 123. All forms of co-ordinate compound judgments 
may occur as premises in inferences. In these inferences 
the same figures are to be distinguished as in categorical 
inferences. Their validity may be proved by reduction 
to the corresponding simple inferences. The like holds 
good of those judgments in which several of the elements 
subordinate to the principal proposition are co-ordinate 
to each other, as well as of those in which the relations 
of co-ordination and subordination of judgment are 
somehow connected with each other. 

The CATEGORICAL-DISJUNCTIVE and the HYPOTHETICAL- 
DISJUNCTIVE inferences are to be taken as examples of 
mixed inferences. The most prominent example is dis- 
junctive inference in the stricter sense, or inference to the 
validity ofa definite part by means of the exclusion of all 
the rest (modus tollendo ponens), and inference to the in- 
validity of the others by proving the validity of a definite 


member (modus ponendo tollens). Other examples are 
given in hypothetical inferences of the First and especi- 


ally of the Second Figure from a conjunctive (copulative 
or remotive) and a disjunctive premise, the Dilemma, 
Trilemma, and Polylemma (or the Syllogismus cornutus 
or Complexio). In these inferences it is shown that, 
whichever of the members of the disjunction may be true, 
the same conclusion results (that the opponent, whichever 
of the different possible cases he may choose, must find 
himself in every case forced to the same conclusion). 
These dilemmata, &c., which turn against what they 
themselves enunciate, or which can be applied as a proof 
of the opposite (δίλημμα ἀντίστροφον, reciprocum ), must 
of necessity contain a fallacy either in the premises or in 























456 § 123. Mixed Inferences with 





the form of inference. In the last case the fallacy 
originates in the identification of two conclusions which 
are different although contained in the same words. 


Disjunctive inferences in the wider sense may be formed in 
all figures. A disjunctive inference takes the following form :— 


In the First Figure. In the Second Figure. 
M is either P, or P,, &c. P is either M, or M,, &c. 
Sis M: S is neither M, nor M,, &c.: 
οὖς Sis either P, or P,, &c. .. 5 ἃ not P. 


In the Third Figure. In the Fourth Figure. 

M is either P, or P,, &c. P is M; 

M is S: M is either S, or S,, &c. 

.. Some Sis either P, or P,, .". (At least) something which 
&e. . is either S, or S,, &c. is P. 


Disjunctive inferences strictly so called are those which 
contain one of the two following forms :— 
A is either B or C. 


(2) But Α is not B: 
“AIC 


(1) But a is B: 
.. Als notc 

or: 

But A is not Cc: 

..AISB 


But Ais Cc: 
.°, Als not B 


or which take one of the analogous forms which can be formed 
from more than two members of disjunction. 

Disjunctive inferences of this kind essentially agree with 
those hypothetical inferences explained in the foregoing para- 
graphs; for the disjunctive major premise is only the compre- 
hension of the following hypothetical judgments :— . 


If A is not B it is Cc, and 
If A is not ὁ it is B. 


If a is Bit is not C, and 
If a is C it is not B. 


The modus ponendo tollens follows the scheme of the First 
Figure, the modus tollendo ponens can be reduced both to the 


Co-ordinately complex Premises, ete. 457 





First and the Second Figures. The Third and Fourth Figures, 
however, do not come into application for the same reason as in 
hypothetical inferences. 

The DILEMMA, in the stricter and special sense, is an infer- 
ence of the Second Figure, with an hypothetico-disjunctive 
premise (which is sometimes major, sometimes minor premise) 
and with a remotive premise. In the wider sensé of the 
term, inferences with a categorico-disjunctive premise and 
inferences in the First Figure with a disjunctive and a 
copulative or remotive premise are also attributed to it. The 
like holds good of the Trilemma, Tetralemma, and Polylemma. 
The forms of the Dilemma in the Second Figure— 


(a) with categorical premises, are: 
(1) a is either Bor C; 
D is neither B nor C: 
.. Dis not A. 


(2) A is neither B nor C; 
D is either Bor C: 
εἷς. Dis not A. 


(b) with hypothetical premises : 


(1) If a is, either B or C is; | (2) If a is, neither B nor c is, 
If op is, neither| Neither B nor | If b is, either | Hither B or c 
BnorCis: | Cis: B or C is: is: 
*. df Dis, Ais] .°. A is not ες If Dis A is|.°. A is not. 
not. not. 








An inference in the First Figure may be considered to be a 
Dilemma, whose major premise is conjunctive—either copula- 
tive: A as well as B is C, and in the hypothetical form : If A is, 
as well as if B is, C is,—or remotive: Neither A nor B is C, and 
hypothetically: Neither if A is, nor if B is, is C; and whose 
minor premise is disjunctive: D is either A or B,and hypo- 
thetically: If D is, either A or B is—or: Now either A or B is; 
from which the conclusion is to be drawn according to the 
moods Barbara and Celarent. These inferences of the First 
Figure, however, both in the categorical and hypothetical forms, 
are to be denoted as inferences of induction. Hence, if they 
are to be called Dilemmata, they must be subsumed under both 
of those logical notions whose spheres partially coincide. This 

















458 $ 123. Mixed Inferences with 





relation must always be avoided if the construction of the ter- 
minology could result purely according to a scientific point of 
view. But the name Dilemma, in its transmission, has been 
inseparably connected with certain examples which can only 
naturally be represented in the hypothetical forms of the First 
Figure. 

Modern logicians waver between more limited and wider 
definitions of the term. Herbart, for example,! limits them to 
the Second Figure, but denotes by the term categorical as 
well as hypothetical disjunctive inferences, | 

Twesten? gives the name Dilemmata to inferences in the 
hypothetical form only, but reckons among them hypothetical 
inferences of the First Figure, with negative major premise and 
conclusion (whose scheme follows the analogy of the mood 
Cesare, but is called Diprese by Twesten, following Lambert). 

With Drobisch® only hypothetical inferences are Dilemmata, 
but they include positive as well as negative inferences of the 
First Figure. 

[Hamilton defines the Dilemma to be a hypothetico-disjunc- 
tive reasoning whose major premise is both hypothetical and 
disjunctive, and whose minor denies the whole of the disjunctive 
consequents, e.g.: If A is B,eitherc is Ὁ, orEisF; but neither 
Ο is D, nor Eis F: Therefore A is not B. 

Mansel defines the Dilemma to be a syllogism having a con- 
ditional major premise with more than one antecedent, and a 
disjunctive minor. Its different forms are :-— 


I. Simple Constructive. 
If Ais B,C is D; andif Eis F, Cis Ὁ; 
But either A is B, or E is F: 
CHR 


II. Complex Constructive. 
If ais B, CisD; andifEisF,GisH; 
But either A is B, or E is F: 
... Either C is Ὁ, or G is H. 


1 Lehrbuch, etc., § 69. 2 Logik, § 150. 
3 Logik, 3rd ed. § 101. 


Co-ordinately complex Premises, ete. 459 





III. Destructive (always complex). 
If Ais B, Cis D; and if Eis F, Gis H; 
But either c is not D, or G is not H: 
εἰς Either A is not B, or E is not F.'] 


Others proceed in other ways. 

The Dilemma, Trilemma, &c. is a perfectly correct form of 
knowledge, when used scientifically. It is no objection to its 
significance in Logic that from antiquity down to the present 
day it has been used constantly for rhetorical ends, and to dis- 
play one’s wit. An example of its scientific value is given in 
the mathematical inference which is true of parallelograms of 
equal height but of unequal and incommensurable bases. 
If the content of the first is not related to the content of the 
second, as the base of the first to the base of the second, they 
must either be related as the base of the first is to a line which 
is greater than the base of the second, or as it is related to a 
line which is smaller than the base of the second. But neither 
the one nor the other proportion is probable. Hence the rela- 
tion of the content must be equal to the relation of the bases. 
In the same way the foundation of the Leibnizian Optimism is 
a scientifically justifiable trilemma. If the actually existing 
world were not the best of all possible worlds, then God did not 
either know the best, or could not create and preserve it, or did 
not wish to create nor preserve it. But (because of the divine 
wisdom, omnipotence, and goodness) neither the first, second, 
nor third is true. Hence the actual world is the best of all 
possible worlds. 

Disjunctive inferences were originally subsumed as a species 
under the notion of the hypothetical. 

Alexander of Aphrodisias says:? ἐξ ὑποθέσεως yap καὶ ot 
διαιρετικοί, of καὶ αὐτοὶ ἐν τοῖς κατὰ μετάληψιν ἐξ ὑποθέσεω-. 

Philoponus,? where he gives an account of the older Peripa- 
tetics and Stoics, distinguishes in those hypothetical syllogisms 
whose conclusion is a categorical judgment (and which thus 


[! Artis Logicae Rudim. p. 108 n.] 


2 Ad Arist. Anal. Pr. fol. 133 5. 3 Ad Anal. Pr. fol. ix. B. 


— — Pin 
m rer 


“«...ὕ.-. PAM E "5... τ 7 
"στ Zr Tr er eS eee -- an 


on 55 
en τ σα: 
= 


Rn Hr 











BE tr on Et 


ae 
eee ee 








460 $ 123. Mixed Inferences with 





form the opposite of the δι’ ὅλου or διὰ τριῶν ὑποθετικοί) the 
ἀκολουθία and the διάξευξι-. 

Boéthius' refers the following division of hypothetical syllo- 
gisms to Eudemus: “ aut tale acquiritur aliquid per quandam 
inter se consentientium conditionem, quod fieri nullo modo 
possit, ut ad suum terminum ratio perducatur (the apagogical 
method of inference), aut in conditione posita consequentia vi 
coniunctionis (the συνημμένον or the ἀκολουθία) vel disiunctionis 
(the διάξευξι5) ostenditur.’ But it is very doubtful whether the 
older Peripatetics, and Theophrastus and Eudemus more espe- 
cially, enunciated in a similar way, as the Stoics did later, five 
fundamental forms of the ‘ hypothetical’ syllogisms leading to 
a categorical conclusion.” 

The Stoic Chrysippus? placed five συλλογισμοὶ ἀναπόδεικτικοι 


at the head of his Logic. The two first of these agree with the , 


modus ponens and modus tollens of inferences formed from an 
hypotheiical and a categorical premise. If the first is, the 
second is; but the first is: Therefore the second is—and: But 
the second is not: Therefore the first is not. The third of 
these syllogisms has a conjunctive major premise of a negative 
form. There is not at the same time the first and the second 
—from which, by means of an affirmative (but not by means of 
a negative) πρόσληψις, an inference can be formed, viz.: Now 
the first is: .*. the second is not. The fourth and fifth infer- 
ences rest on a disjunctive major premise: Either the first is 
or the second—from which in two ways, by means of an affirm- 
ative and also by means of a negative πρόσληψις--(1) Now 
the first is: .*. the second is. not; or (2) Now the second is 
not: .*. the first is. 

The Dilemma was first explained by the rhetoricians. 

Cicero says:* complexio est, in qua utrum concesseris, 
reprehenditur. 

ı De Syllog. Hypoth. p. 607. | 

2 Prantl imagines they did, Gesch. der Log. i. 379 ff., 385 ff. ; οἵ. 
473 ff. 

3 According to Sext. Emp. Adv. Math. viii. 223; ef. Hyp. Pyrrl. 
ii. 157 sqq. 

4 De Invent. i. 29, 45. 


Co-ordinately complex Premises, ete. 461 





Quintilian teaches :' fit etiam ex duobus, quorum necesse 
est alterutrum, eligendi adversario potestas, efficiturque, ut, 
utrum elegerit, noceat. 

The rhetorician Hermogenzs has the term: διλήμματον 
σχῆμα "---διλήμματον δὲ σχῆμά ἐστι λόγος ἐκ δύο προτάσεων 
ἐναντίων τὸ αὐτὸ πέρας συνάγων. 

The most noted examples transmitted of rhetorical sophis- 
tical dilemmas are the anecdote of Korax and Lisias about 
instruction in the art of persuasion:* ὦ Κόραξ, τί ἐπηγγείλω 
διδάσκειν ;---τὸ πείθειν ὃν ἂν θέλῃς "---εἰ μὲν τὸ πείθειν με ἐδίδαξας, 
ἰδοὺ πείθω σε μηδὲν λαμβάνειν " εἰ δὲ τὸ πείθειν με οὐκ ἐδίδαξας, 
καὶ οὕτως οὐδέν σοι παρέχω, ἐπειδὴ οὐκ ἐδίδαξάς με τὸ πείθειν ; 
—the similar story of Protagoras and Euathlus about the 
honorarium to be paid by the latter to the former when he 
gained his first case ;4—the fallacy in the dialogue between a 
crocodile and the father or mother whose child has been seized, 
called ὁ κροκοδειλίτης or ἄπορος *—and the dilemma of Bias: εἰ 
καλήν, ἕξεις κοινήν" et δὲ αἰσχράν, ἕξει5 ποινήν.5 The ψευδόμενος 
already mentioned’ is of the same kind. 

The solution of the ἀντιστρέφοντα in these dilemmas depends 
on the division of the apparently simple conclusion into the 
two elements which it contains. In the law case of Protagoras 
and Euathlus (as Bachmann® and Beneke® have rightly re- 
marked) a different decree must be given in two different con- 
clusions. In the first place, the condition of the bargain was 
not fulfilled. Euathlus has until now won no case, and so is 
not yet obliged to pay the sum. Hence he must gain this case. 
But by this decision the state of the case is altered, and Pro- 
tagoras must be allowed to bring a second action, on the ground 


I Inst. v. 10, 69. 

? De Inv. iv. 6; cf. Anon. Prolegom. ad Hermog. iv. 14. 

° Anon. Prolegom. ad Hermog. iv. 14. 

* Schol. ad Hermog. p. 180, ed. Walz; Gell. v. 10. 
| ° Diog. Laert. vii. 44, 82; Lucian, Βίων πρᾶσ. 22: in another form, 
instead of the crocodile the robber of the daughter of a soothsayer, 
Schol. ad Hermog. pp. 154, 170. 

® Gell.v. 11; cf. ix. 16, δ. 7877. 

* System der Logik, p. 248. 9 System der Logik, p. 140. 


— ie nn ng 
= 


ee - 
ba - -- μα. τοι τς ze x 
- ge ᾿ u " ‘ 














462 § 123. Mixed Inferences with Co-ordinately, etc. 








of the changed relation, which must be decided in his favour. 
It must be granted without hesitation that cases may occur 
where the logical distinction cannot actually be realised (as 
e.g. in the anecdote of the crocodile, the death of the stolen 
child would make any further action needless). For if ab- 
surdity once enters into the premises, it must appear in the 
conclusion. 

Boéthius, like the earlier logicians, reckons disjunctive 
judgments and inferences among the hypothetical: fiunt vero 
propositiones hypotheticae etiam per disiunctionem ita: aut hoc 
est, aut illud est ;—omnis igitur hypothetica propositio vel per 
connexionem (per connexionem vero illum quoque modum, qui 
per negationem fit, esse pronuntio), vel per disiunctionem.' 
He puts both of these forms or the whole hypothetical or con- 
ditional judgments and inferences in the wider sense as the 
complex in opposition to the categorical or predicative as the 
simple: praedicativa simplex est propositio; conditionalis vero 
esse non poterit, nisi ex praedicativis propositionibus coniunga- 
tur ;—ac de simplicibus quidem, i.e. de praedicativis syllogismis 
duobus libellis explicuimus ;—non simplices vero syllogismi 
sunt, qui hypothetici dieuntur, quos Latino nomine conditio- 
nales vocamus ;—necesse est, categoricos syllogismos hypothe- 
ticis vim conclusionis ministrare.? | 

Later logicians have made disjunctive judgments and in- 
ferences co-ordinate with the hypothetical, because they have 
taken the latter term in its narrower sense, but have subsumed 
both, with Boéthius, under the notion of the not simple or com- 
pound, and so opposed them to the categorical, which are simple 
and primitive. 

This plan prevails in the Cartesian and also in the Leib- 
nizian Schools. The frequently mentioned Logique ou l’Art de 
Penser ὃ divides syllogisms into simple (simples) and compound 
(conjonctifs); the former (as in $ 120, p. 444) are divided into 
incomplexes and complexes, the latter‘ into conditionnels, dis- 
jonctifs, and copulatifs. The individual forms essentially 


1 De Syll. Hypoth. p. 608. 2 Ibid. p. 607. 
3 Part ii. ch. 11. 4 Ch. xu. 


§ 124. Compound Inferences, etc. 463 





agree with the five συλλογισμοὶ ἀναπόδεικτοι of Chrysippus 
(see p. 460). 

Wolff says:' syllogismus compositus est, cuius vel una, vel 
utraque praemissa non est propositio categorica ; he enumerates 
here ? the hypothetical (syllogismus hypotheticus, conditionalis, 
connexus) and ® the disjunctive syllogism (syllogismus disiunc- 
tivus ). 

Leibniz himself subsumes disjunctive inferences under the 
hypothetical, after the fashion of the Peripatetics.‘ 

Kant? first enumerates categorical, hypothetical, and dis- 
junctive syllogisms as three co-ordinate kinds, which he refers, 
as he does the corresponding judgments, to three supposititious 
original and primary notions of the understanding; viz. to the 
three categories of Relation—Substantiality, Causality, and 
Reciprocity. He abandons the view that the categorical in- 
ferences of reason are regular and the others irregular ; for all 


three kinds are the products of equally correct and essentially 
mutually distinct functions of reason. 


This division suffers from the same defects as the correspond- 
ing division of judgments (cf. § 68). Kant, however, is correct 
when he denies that these inferences as such are compound. 


§ 124. CoMPOUND INFERENCES are combinations of 
simple inferences by means of common parts, through 
which a final judgment (mediately ) is deduced from more 
than two given judgments. The individual parts of 
the compound inference are either completely or incom- 
pletely expressed. In the first case, the Chain syllogism 
arises (syllogismus concatenatus, catena syllogismorum, 
polysyllogismus). This is a series of inferences so 
linked to each other that the conclusion of one makes 
a premise of the other. That inference in which the 


) 
Log. $ 403. 2 Ibid. $ 404. 3 Ibid. § 416. 


4 47 M 
; Nouv. Ess. iv. 17, p. 395 in Erdmann’s ed. of the Philosophical 
Works. 


5 a 
Log. § 60; Krit. der r. Vern. Elementarl. §§ 9, 19. 














τας πε a — i al = ut - - 


a zug 





464 § 124. Compound Inferences. The Chain of 





common proposition is the conclusion is called Prosyllo- 
gismus, and that in which it is the premise, Episyllo- 
gismus. The advance from the prosyllogismus to the 
episyllogismus (a principiis ad principata) is called epz- 
syllogistic, or progressive, or synthetic, and the advance 
from episyllogismus to prosyllogismus (a principiatis 
ad principia) is called prosyllogistic, or regressive, OY 


analytic. 


Thus, e.g. Boöthius! concludes episyllogistically or pro- 
gressively, for he first forms the syllogism: what furthers 
(prodest) is good ; what exercises or improves, furthers: There- 
fore what exercises or improves is good,—and continues using 
the conclusion attained as a premise (the major premise) of a new 
syllogism : misfortune, which happens to the good, serves either 
(if he is a wise man) to train him, or (if he is a proficient) 
to improve him. Hence misfortune which befalls the good 
is good. 

In the long mathematical example § 110, the conclusion 
of 1 is minor premise in 3; the conclusion of 3 is minor 
premise in 4, and so on. In this reference the course of 
demonstration is progressive. This chain of inference is epi- 
syllogistic or progressive. If there is amedium obstructing the 
motion of the planets, then the path of the earth cannot be 
constant nor periodical, but must always become less: If this 
be the case, then the existence of organisms on the earth cannot 
have been (nor can remain) eternal. Hence, if there is this 
medium, organisms must have at one time come into existence, 

and will wholly pass away. If organisms once existed for the 
first time on the earth, they must have arisen out of inorganic 
matter. If this is the case, there has been an original: produc- 
tion (generatio aequivoca). Hence, if this obstructive medium 
exists, there has been an original production. 

Cato argues prosyllogistically or regressively in Cicero: κ 


1 De Consol. Philos. iv. pt. vii. 2 De Fin. iii. 8, 27. 





Inferences. The Prosyllogism, etc. 465 


quod-est bonum, omne laudabile est; quod autem laudabile 
est, omne honestum est: bonum igitur quod est, honestum est. 

This syllogism is supported by a supplementary proof of a 
premise (the minor: quod est bonum omne laudabile est). 

If the major premise be proved supplementarily, the inference 
is also made prosyllogistically or regressively. The historical 
development of the sciences in its length and breadth should 
take this course. For certain general propositions are first dis- 
covered (as, e.g. the laws of Kepler) under which the individual 
facts are syllogistically subsumed. The highest principles 
are discovered later (e.g. the Newtonian law of Gravitation) 
from which those general propositions are necessary deductions. 
A like course is to be preserved in many cases for didactic 
reasons in the exposition of the sciences. In psychology a 
similar significance might belong to the fundamental T»- 
cesses of Beneke—the formation of sensations in consequence 
of external affections, the formation of traces or unconscious 
constructions of memory, of the internal affections, to which 
also belongs the calling into consciousness of like thoughts by 
the like, and the reconstruction of mental (psychic) Be 
which belongs in Astronomy to Kepler’s laws; for from these 
processes the individual phenomena of the mental (psychic) life 
may be genetically explained. The prosyllogism which de- 
duces these processes from higher principles has yet to be 
sought for. The Herbartian hypotheses, which, even if they 
were correct, could not be placed in the same rank with the 
principles of Newton, are insufficiently established, and, al- 
though enunciated to avoid contradictions, are not free from 
internal contradiction. (The monads or the real essences are 
not in space, and yet are the substantial elements of what exists 
in space; self-maintenance suffices only to maintain what 
exists, and yet is sufficient to establish the new, which remains 
as a conception after the removal of the existing cause, and 
affects in manifold relations other results of ET TREIBEN 
Hence they are untenable. 

The exposition of the different forms which a combination 
of syllogisms admits or excludes, whether they take the form 


H H 


LT ET DE “ὦ daten 


———— = - 
ae eh νον ὕειν en gen mung 


et eS ee 
= 


i 
N 


͵ 


Ϊ 
1. 
; 


Ht 
ig! 
Ἢ 


ne ee 


ee 
wt ee 


: ee 
u m.” 


—_ 


= lt cl - 




















466 § 125. Simple and Complex In ferences 














of inferences of the First or the other Figures, appears to be 
unnecessary, for the general syllogistic rules enable us to deal 
securely with every given case in the enunciation and testing 


of chains of reasoning. 


§ 125. An ENTHYMEME (ἐνθύμημα, syllogismus decur- 
tatus) is a simple inference abbreviated in the en 
by the omission of one of the two premises. The pre- 
mise which remains unexpressed must be completed in 
thought, and thus the enthymeme is logically equivalent 
to a fully expressed syllogism. If one-or both of the 
premises of a simple inference be enlarged by the —_ 
tion of reasons, the ErıcHEIREMA results (ἐπιχείρημα, 
aggressio), which is, therefore, an abbreviated compound 
inference. The abbreviation, however, has to do only 
with the form of the syllogism reduced to a subordinated 
proposition which is given as the cause of one of the 
premises. 

An episyllogistic chain of reasoning whose ane 
is simplified by the omission of all the conclusions ae 
the last, and where those suppressed conclusions ase 
identical with the major or minor premises of the fol- 
lowing syllogisms, is called a Chain-syllogısm or 8 

SORITES (σωρείτης, sorites, acerbus, syllogismus acer- 
vatus). The Aristotelian Sorites differs from the = 
clenian by the arrangement in which the premises fol ow 
each other. The former has the form: A 18 B, Β 15 C, 
cisD: .. AisD. It advances from the lower notion 5 
the higher. The minor premises of all the syllogisms 
save the first (e.g. A is c) are not expressed, but are Ὁ 
be added in thought in the analysis which completes 
them. The Goclenian Sorites, on the other hand, has 


. . ς . ._ A is 
the opposite succession of premises: C 18 D, Bl C, 


expressed in an Abridged Form, etc. 467 


B: .‘. Ais D. It advances, so far as the succession of — 
premises is concerned (and if, as in Aristotle’s Sorites, 
the predicate be enunciated before its subject, so far as 
the succession of notions also is concerned), from the 
more universal to the less universal. - The major pre- 


mise of all the syllogisms except the first (e.g. B is D) 
is to be added in thought. 





The scheme may be given for the sake of distinctness :— 


Aristotelian Sorites. Goclenian Sorites. 


‘ ee: = Go =D 
B is 
Ο is 
A 


is 
Analysis. Analysis, 
l. A is B (minor premise) 


l. C is D (major premise) 
B is C (major premise) 


RB ἮἘ ¢ (minor premise) 


A is ἃ (conclusion) D (conclusion) 


2. A is C (minor premise) 


D (major premise) 
C is D (major premise) 


B (minor premise) 





A is D (conclusion) D (conclusion) 


In the Aristotelian Sorites that conclusion which in the 
following (or in a great number of members, in each of the 
following) syllogism becomes the minor premise is not ex- 
pressed (but is to be added in an analysis which completes the 
thought). In the Goclenian Sorites that conclusion which in 
(each of) the following syllogisms becomes the major is omitted. 
Both forms, the Aristotelian and Goclenian, agree in this, that 
the conclusion of the first syllogism is the premise (major or 
minor) of the second. The characteristic (§ 124) of episyllo- 
gistie procedure lies in this, that one advances from previous to 
consequent inferences. Hence, both in the Goclenian and in 
the Aristotelian Sorites the advance is episyllogistic. Itisa 
mistake to think the Goclenian prosyllogistic or regressive. 

HH 2 














. 


4608 $125. Simple and Complex Inferences 





The Enthymeme must not be considered to be an immediate, 
nor the Epicheirema a simple influence. The abbreviation of 
expression does not change the form of thought. 

Examples of Chain-syllogisms may be seen in great numbers in 
scientific writings which advance from given hypotheses to final 
results. In such writings the form of a chain of thoughts is more 
frequently shortly ‘ndicated than completely expressed accord- 
ing to the logical schematism. For example, Aristotle’ concludes 
that the exposition of action, the combination of events into the 
unity of a complete action or the μῦθος, is the most important 
of the elements of Tragedy, from the following premises: 
Action is that in which happiness lies ; what contains happi- 
ness is the end and aim; the end and aim is what is highest: 
Therefore action is what is highest. This is true in actual 
life. But the unspoken thought must be added: The re- 
production of what is actually the highest in the objects repro- 
duced in Tragedy (Action, Character, Thought) is the highest 
in Tragedy. Hence it follows that, because action is highest 
in real existence, its reproduction or the μῦθος is highest in 
Tragedy. In the same sense Aristotle concludes negatively 
that the reproduction of character is not highest : Character isa 
quality (a ποιόν) ; Quality is not that in which happiness lies ; 
that in which happiness does not lie is not the end: What is not 
the end is not highest. The unexpressed thought must be added : 
The reproduction of what is not actually highest in what is to 
be reproduced in Tragedy, is not highest in the work of art. 

Aristotle does not, like later logicians, mean by ἐνθύμημα 
an abbreviated inference, but an inference of probability. He 
says :? ἐνθύμημα μὲν οὖν ἐστι συλλογισμὸς ἐξ εἰκότων ἢ ση- 
μείων. He classes it? among the rhetorical syllogisms. The 
Enthymeme, in the Aristotelian sense, when compared with 
the scientific or apodictic syllogism, is a mere previous deli- 
beration or consideration producing only subjective conviction 
(and so the name signifies, although moderns have strangely 
made it refer to the retention of one premise in the mind, 


2 Anal. Pr. ii. c. xxvii. p. 70 A, 10. 
3 Anal. Post. i. 1, p. 71 A, 10. 


1 Poet. c. vi. 


expressed in an Abridged Form, ete. 469 





ev θυμῷ). It is an imperfect form of inference, and therefore 
has been called by some logicians (according to Quintil. Inst 
Or. v. 10) ‘imperfectus Syllogismus.’ The εἰρῳροθρίνα 
has been taken to mean imperfection of expression by lat 
logicians. ΓΙ 
Boéthius also says in this sense: 2 Enthymema est imper- 
fectus syllogismus, i.e. oratio, in qua non omnibus antea ER 
positionibus constitutis infertur festinata conclusio, ut si = 
ah animal est ; substantia igitur est. The ἐπιχείρημα 
is, in Aristotle, an inference which tests, συλλογισμὸς διαλεκ- 
rıcos.® It is often useful, in debated questions, to reason 
by means of a double ἐπιχείρημα, both from the proposition 
and from its negation, not to be brought sophistically to a stand- 
still by the contradiction, but in order to gain dinkeotiodd ex- 
perience, and, by breaking through the illusion in this way, to 
come to a sure settlement of the question.4 There has eon 
some uncertainty amongst the later logicians and rhetoricians 
more especially among the Latins, about the meaning of the 
term. Quintilian® ascribes the translation PERLE to 
Valgius, and the explanation of the Epicheirema as an ‘ apo- 
dixis imperfecta’ to Caecilius. This explanation is whee to 
the meaning of Aristotle, but does not exhaust it. According 
to the later logicians, the Epicheirema agrees with the Enthy- 
meme in this, that the imperfection contained in it lies in the 
incompleteness of expression, but the Epicheirema is dis 
tinguished from the Enthymeme by denoting a certain EEE 
viation of the compound (or extension of the simpl 
logism. u 
The term SORITES is not found in Aristotle® in the sense 
Er above. It came into use later. Cicero, for ie 
uses it,’ calling it the inference of the Stoics: quod Kan 


' [This question is full : 
| a y and clearly discussed by Hamilt 
on Logic, i. 888, and Discus. p- 154. | EEE 


2 


πῇ ed. Basil. Ρ. 864. 3 Top. viii. 11, p. 162 a, 16. 
id. c. xiv. p. 163 A, 36 ff. 5 Inst. Orat. v. 10. 


He: eS ing i 
He indes to the thing itself, Anal. Pri. i. c. xxv. 
De Fin. iv. 18, 50. 


4 


6 





de - 


ng «πων ὦ — u ee ne eng 


- 
F 
J 
ἢ 

| 


> u u BR mn 
rae ' 

















470 § 126. Paralogisms and Sophisms. 





sit, id esse optabile; quod optabile, id esse expetendum ; quod 
expetendum laudabile ;—igitur omne bonum laudabile. The 
Goclenian Sorites is not essentially distinct from the so-called 
Aristotelian, and corresponds strictly to the Aristotelian Syl- 
logism. It gets its name from Rudolf Goclenius (1547-1628), 
Professor at Marburg, who first explained this form in his 
Isagoge in Organum Aristotelis, 1598. In this work he 


partially follows Ramus. 
[Hamilton accepts the justness of these two forms of the 


Sorites as a testimony in favour of the scientific accuracy of 
his distinction between reasoning in comprehension and reason- 
ing in extension. The Goclenian Sorites, in which the subject 
is the containing whole, and the predicate the contained part, 
proceeds in the Quantity of Comprehension ; the Aristotelian 
Sorites, in which the predicate is the containing whole, and 
the subject the contained part, proceeds in the whole of Er- 


tension.'] 
I," 


$ 126. An inference incorrect in its formal relation 
(fallacia) is a PARALOGISM if it leads the person reasoning 
into error. If there is the intention to deceive, it is 
called a sormısm. Formal fallacies depend partly on a 
false comparison of spheres, and partly on the ambiguity 
of the signification of one and the same notion, more 
especially of the middle notion. The Fallacies of the 
First kind, which are most worthy of notice, are— 


Inferences with a negative minor premise in the 
First Figure, 

Inferences with affirmative premises in the Second 
Figure, 

Inferences with an universal conclusion in the 
Third Figure; and 


[! Cf. Hamilton’s Lect. on Logic, i. 380. | 


δ 126. Paralogisms and Sophisms. 471 





The Fallacia de consequenti ad antecedens in cate- 
gorical and hypothetical form. 


The Fallacies of the Second kind are divided into— 


(a) Fallaciae Secundum dictionem, and (b) Falla- 
ciae extra dictionem. 


(a) Among the former are reckoned those which 
proceed from— 


Homonymia—i.e. from similarity of name in dif- 
ferent things which have no similarity of notion, 
and where there is, therefore, an ambiguity in 
the word. The fallacy arises from the reciprocal 
exchange of the different meanings of the same 
word. 

Prosodia—the fallacy arises from the exchange of 
words which sound similarly and have the same 
letters, but are differently accentuated. 

Amphiboly—ihe mistaking syntactical forms which 
have a double sense. And from 

Figura dictionis (σ χῆμα τῆς λέξεως )—the mistaking 
the grammatical form of individual words, espe- 
cially the interchange of different forms of in- 
flection, of different parts of speech, and of 
different forms of conception or categories in the 
Aristotelian sense of the word. 


(b) To the Fallaciis extra dictionem belong more 
especially — 


Fallacia ex accidente—an interchange of the essen- 
tial and non-essential. 


Fallacia a dicto secundum quid ad dictum simpliciter; 








- Sr I A Bi 


§ 126. Paralogisms and Sophisms. 

















and conversely, a dicto simpleiter ad dictum 
secundum quid—an interchange of the absolute 
and relative senses of the term considered. 

Fallacia secundum plures interrogationes ut unam 
—nevlecting the necessity of dividing a question 
which, according to its different references, re- 
quires several answers. 


All fallacies of the second kind contain a more or less 
hidden quaternio terminorum—1.e. four principal terms 
—or a Saltus in concludendo—i.e. a leap or hiatus in 


arguing. 


The doctrine of fallacies has a more didactic and historical 
than a peculiarly’ scientific interest. Logic, as the science of 
thinking and knowing, gives an exposition of the normative 
laws. Whatever contradicts these laws is fallacious. To 
enumerate exhaustively all the possible departures from 
these rules would be a useless waste of work, for error ıs an 
ἄπειρον. 

It is sufficient to exemplify the kinds of fallacies which even 
practised thinkers often fall into. 

When Descartes believed that matter in opposition to mind 
was without foree—entirely passive, a form of thought under- 
lay his belief which, when brought to the form of a simple 
syllogism, can be represented as a fallacy in the First Figure 
with a negative minor premise. Mind is active; matter 1s not 
mind: .". matter is not active. Many defences of negro slavery 
proceed upon this fallacy. Caucasians have the rights of men; 


Negroes are not Caucasians: .". They have not the rights οἱ 


men. 
The fallacy resulting from merely affirmative premises ın the 


Second Figure is exemplified in the inference that the ao. 
state is essentially identical with the old Hellenic, because both 
agree in requiring the unconditional submission of the individual 
ads = , 5 72 
to the community. (The inference overlooks the essential dif 


§ 126. Paralogisms and Sophisms. 473 





ference of the immediate unity in and through a community of 
disposition, and subordination. under a scholastically fostered 
transcendental wisdom. ) 

In the Third Figure a universal conclusion would be falsely 
drawn in the reasoning: All men are inhabitants of the earth; 
all men are reasonable creatures; all reasonable creatures are 
inhabitants of the earth. 

When from the material truth of certain consequents the 
validity of the presupposition is inferred, the fallacy de con- 
sequente ad antecedens results. It is exemplified in the fol- 
lowing. Helmholtz! enunciates the proposition: whatever in 
sense-perception is overcome and converted into its opposite 
in the intuition-picture by moments which experience has 
given, undoubtedly cannot be recognised to be sensation (but 
must be considered as a product of experience and practice). 
This proposition is equivalent to the proposition from which it 
proceeds (ὃ 87) by conversio simplex: whatever in the sense- 
perception is sensation cannot be overcome (set aside and con- 
verted to its opposite) by moments of experience. Now an- 
other author? gives the following proposition as the equiva- 
lent of this. Everything in our sense-perception that is not 
overcome and converted into its opposite by the moments of 
experience in the intuition-picture, is sensation. But this pro- 
position is in fact by no means identical with that of Helmholtz. 
It can only be made equivalent to it by means of the paralogism 
we are illustrating. The real consequence is only: Something at 
least which cannot be overcome by the moments of experience is 
sensation (cf. ὃ 91 or§ 85). If we believe, with Helmholtz, that 
whatever is sensation, cannot be overcome by the moments of 
experience (sensation being the antecedens, and the impossibility 
to be overcome the consequens), the assertion is still not equi- 
valent to this, that sensation always is present where this im- 
possibility to be overcome exists. For this same impossibility 
to be overcome might arise from something else which is not 
sensation, perhaps from what is ἃ priori, in the Kantian sense of 


' Physiol. Optik. p. 488, Leipzig, 1867. 


2. Böhmer, Die Sinneswahrnehmung, p. 617, Erlangen, 1868. 





τὸν αν nen 
--- - 


ee ay mu 


- .- σ΄ 





— ein 





ee Ee eee 





| 
} 
ΩΣ 
N 
bi 


“- 


Az 


TV en nn ame oe ET m 4 


474 § 126. Paralogisms and Sophisms. 





the word, or to what had been so firmly established by earlier 
experience that no later experience can alter it. Cf. § 122, 

A concealed quaternio terminorum is the most frequent and 
the most deceptive of fallacies. A fallacy of this kind lies in 
Plato’s inference in the Phaedo: The soul is ἀθάνατος (which 
according to the connection of the passage 18 only proved in 
the sense: according to its essence, so long as it exists, it is 
never dead): Everything ἀθάνατον (i.e. immortal) is ἀνώλεθρον : 
Hence the soul is ἀνώλεθρος. So in the inference of Epicurus : 
Whatever has effects is something ἀληθές ; every perception 
has effects (psychical): Hence it is something @Andes—where 
the same word now means actual, at another time true. A 
quaternio terminorum often lies in the use of such expres- 
sions as boni, optimi, &c. which waver between the meanings 
of: the aristocracy of talent and character, and the aristocracy 
by birth, when debating the best form of government. Ter- 
tullian’s fallacy rests on a quaternio terminorum : It contra- 
diets the conditions of human existence that men should con- 
tinually live with their heads undermost and their feet 
uppermost; those at the antipodes must live in this way: 
hence there are no dwellers at the antipodes. (The first pre- 
mise is true only for an uppermost and undermost understood 
from the stand-point of the individuals concerned, and the 
second true only of an uppermost and undermost understood 
of the stand-point of the speaker). Calov’s inference contains 
a quaternic terminorum : Changes in the vowels of the Hebrew 
text of the Bible are inadmissible and criminal because man, 
liable to error, ought not to touch God’s word (where ‘ God's 
word’ means now, really, the transmitted text of the Bible, 
then, ideally, the Divine Truth). When the Stoies quote as 
an example of impossibility : ἡ γῆ ἵπταται, using flying in the 
proper sense of the word, and at the same time exclude by it 
any motion of the earth, the deceptive form of the expression 
ἵπτασθαι implicitly contains a fallacy of the kind now under 
consideration. Explicitly stated, it would be as follows: 
Whatever moves on in open space (without support from be- 
neath) flies; what has no wings (and therefore the earth) does 


§ 126. Paralogisms and Sophisms. 475 





not fly: Hence what has no wings (and therefore the earth) 
does not move on in open space. Logical analysis reveals the 
fallacy lurking in the double sense of the expression ‘ flying,’ 
and concealed by the enthymemic use of the figurative ex- 
pression. Cf. § 61: Remarks on Synthetic Definitions; and 
§ 137: On Failures in Proof. 

Aristotle, in his Περὶ τῶν σοφιστικῶν ἐλέγχων, is led to give 
especial attention to the sophisms most discussed in his day. 
He defines! the σόφισμα to be συλλογισμὸς ἐριστικός, and divides 
Sophisms into two chief classes: παρὰ τὴν λέξιν and ἔξω τῆς 
λέξεως. In the first class he reckons? six kinds : ὁμωνυμία (aequi- 
vocatio), außıBoAia(ambiguitas), σύνθεσις (fallacia a sensu diviso 
ad sensum compositum), διαίρεσις (fallacia a sensu composito ad 
sensum divisum ), προσῳδία (accentus), σχῆμα τῆς λέξεως (figura 
dictionis). The third and fourth of these, as far as they be- 
long to the fallaciis secundum dictionem, can be classed in 
the above-given sense under the notion of Amphiboly. These 
two are the mutual exchange of mutual and collective sense, 
or of what is true of all individuals, or in every special in- 
dividual reference, and of what is true only of the sum total of 
the individuals.? 

Aristotle enumerates among the sophisms of the Second 
division the following seven kinds: παρὰ τὸ συμβεβηκός (fal- 
lacia ratiocinationis ex accidente), τὸ ἁπλῶς ἢ μὴ ἁπλῶς (a dicto 
simpliciter ad dictum secundum quid), 7 τοῦ ἐλέγχου ἄγνοια 
(ignoratio elenchi), παρὰ τὸ ἑπόμενον (fallacia ratiocinationis ex 
consequente ad antecedens), τὸ ἐν ἀρχῇ λαμβάνειν, αἰτεῖσθαι 
(petitio principii), τὸ μὴ αἴτιον ὡς αἴτιον τιθέναι (fallacia de 
non causa ut causa), τὸ τὰ πλείω ἐρωτήματα ν ποιεῖν (fallacia 
plurium interrogationum). These fallacies, however, are partly 


! Top. viii. 11. 2 De Soph. Elench. c. iv. 
u ne λέξεως Aristotl ] i 
y σχήματα τῆς λέξεως Aristotle means here the grammatical forms 

of nouns and verbs, and in Poét. c. xix. more especially the forms of 
proposition founded upon the various relations of predicate to subject, 
which are partly expressed by verbal moods: Imperative, Desiderative, 
Threatening, Indicative, Question and Answer. 

* Poét. c. v. 











476 § 127. /nduction in General. 





rather fallacies in demonstration (§ 137) and fallacies in single 
judgments than properly fallacies of inference. Aristotle, in 
his Περὶ σοφιστικῶν ἐλέγχων, gives examples of the fallacies 
named by him. Plato’s (or a Platonist’s) dialogue Euthy- 
demus may also be compared. Fries gives ancient and modern 
examples, for the most part made up.' A detailed and ac- 
curate account of fallacies of inference may be found in Mill’s 
Logie.’ 

Trendelenburg very properly remarks, in reference to the 
nebulous, misty character of so many modern speculations, and 
to the innumerable fallacies which apparently solve the insoluble 
problem of deriving perfection from the imperfect, that a 
modern reproduction of Aristotle’s work on the solution of 
fallacies is a want of the day? 

This problem has been attempted by the Antibarbarus Logicus 
of Cajus,* but only in a one-sided way, although the author is 
somewhat skilful in performing certain police duties within the 
province of philosophical thought. 


$ 127. Inpuction (inductio, ἐπαγωγή) is the infer- 
ence from the individual or special to the universal. 
Its form is the following :— 


M,, as well as M, and M,;.... is P 
M,, as well as M, and M,;.... isS 


Every S is P 





This inference proceeds from the individual or particular 
(M), which ever approaches the universal (S) by suc- 


cessive extension to the universal (S). The inference 
of induction in its external form is somewhat like a 
conjunctive syllogism of the Third Figure, but is essen- 


1 System der Logik, § 109. 2 7th ed. ii. 352-401. 
3 Erläut. zu den Elem. der Arist. Log. p. 69, 1842. 
4 1851; 2nd ed. part i., 1853. 


δ 127. /nduction in General. 477 





tially distinguished from it by its endeavour to reach a 
universal conclusion. 


The expression induction is used in the proper and strictest | 
sense, when inference is made from the individual, laid hold of 
by observation, to the universal. The logical form, however, 
is the same when inferences are made from smaller groups to 
the universal which contains them, and this inference also must 
be recognised as inductive. 

The predicate, as well as the subject of the minor premise, 
may be a plurality in the inductive inference. If the predicate 
merely is a plurality, the form would be :— 

M is P 


M iso, as wellaso,ando,... 





Everything that is σ᾽» as well as o, ando,,. .. is P. 
For example: The earth has inhabitants ; the earth is a planet 
of medium size of a medium distance from the sun, surrounded 
by an atmosphere whose meteorological phenomena are subject 
to regular returns: Therefore every planet of the same kind 
has inhabitants. 

This inference advances from the individual or particular 
(M) to a universal (σ) which approaches (M) by successive 
limitations. It has not, however, the peculiarly inductive 
character in so far as the ‘ everything this is σὴ» as well as a,, 

. is, does not yield a truly singular universal notion. The 
same would be true in the combined form :— 


M,, as well as M,, . . . is P. 
M,, as well as M,,... is botho, ando,... 


Everything which is σ᾽» as well as o,, . . . is P. 


All these forms may also occur in hypothetical inferences. 

The following inference may here serve as an example of 
induction: The planet Mars moves (as Kepler has proved) in 
an elliptical orbit round the sun. The planet Jupiter does so 
also, ἕο. Hence it is to be concluded that the planets generally 
move in an elliptical orbit round the sun. Other examples will 
be contained in the following paragraphs. 








478 § 127. /nduction in General. 





Aristotle traces the first methodical use of Induction back to 
Socrates (ὃ 12). The use of the expression éravayew in 
Xenophon’s Memorabilia! is worth noticing. It is there said 
of Socrates, that if anyone contradicted him without alleging 
his reasons, he always went back to his presuppositions. For 
example, if the question arose—What citizen is the better, 
Socrates first sought to find out what was the work of a good 
citizen in the government of the state, in war, in embassies, 
and so on:—émi τὴν ὑπόθεσιν ἐπανῆγεν ἂν πάντα τὸν Aoyov' 
» + + οὕτω τῶν λόγων ἐπαναγομένων καὶ τοῖς ἀντιλέγουσιν 
αὐτοῖς φανερὸν ἐγίγνετο τἀληθές. This is going back to the 
universal not for its own sake, but in order to infer something 
else from it. In like manner Plato, in the dialogue Phaedo,? 
makes Socrates demand that those in debate go back from a 
debated proposition to more general and more certain presup- 
positions. The Socratic ‘ Induction’ in the Aristotelian sense 
does not lie in this procedure, but in the combination of in- 
dividual and similar facts whereby a universal proposition 
arises from the former which becomes certainty. For example, 
the pilot who understands his business is the most skilful, the 
physician who understands his business is the most skilful, and 
thus in all departments he who understands his business is the 
most skilful. | 

Plato, like Socrates, makes the comprehension of indi- 
viduals in the general serve for the formation of notions :?—eis 
μίαν TE ἰδέαν συνορῶντα ἄγειν τὰ πολλαχῆ διεσπαρμένα, ἵνα 
ἕκαστον ὁριζόμενος δῆλον ποιῇ περὶ οὗ ἂν ἀεὶ διδάσκειν ἐθέλῃ. 
Induction is a mode (εἶδος) of procedure of philosophical think- 
ing which forms the natural presupposition of the opposite 
method,—deduction from universals to particulars. The method 
of Abstraction, by which universal notions are formed, and of 
Induction, by which universal propositions are formed, appear 
in Plato not yet distinguished from each other. 

Aristotle calls Abstraction ἀφαίρεσις," and Induction ἐπαγωγή. 
He defines Induction thus :ὅ ἐπαγωγὴ ἡ ἀπὸ τῶν Kal’ ἕκαστον 


I iv. 6, 13, 14. =P. Ts. 3 Phaedr. 265 D. 
4 Anal. Post. i. 18 and passim. 5 Top. i. 12. 








δ 127. Luduction in General. 479 


ἐπὶ τὰ καθόλου epodos'— δ᾽ ἐπαγωγὴ ἐκ τῶν κατὰ pépos. 
Aristotle makes Induction in the stricter sense co-ordinate with 
Abstraction, because it leads to the universal judgment or 
proposition, while Abstraction leads to the universal notion. 
He often, however, uses ἐπαγωγὴ in a wider sense, which in- 
cludes Abstraction. The term ἐπαγωγὴ refers to the succes- 
sive enumeration of individual members (rationes inferre). 
Aristotle teaches :*—advvatov δὲ τὰ καθόλου θεωρῆσαι μὴ δι᾽ 
ἐπαγωγῆς, ἐπεὶ καὶ τὰ ἐξ ἀφαιρέσεως λεγόμενα (i.e. the 
mathematical especially) ἔσται δι’ ἐπαγωγῆς γνώριμα ποιεῖν. 
He believes, however, that Induction is more a popular than a 
strictly scientific way of knowledge : φύσει μὲν οὖν πρότερος 
καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμὸς, ἡμῖν δ᾽ ἐναρ- 
γέστερος ὁ διὰ τῆς ἐπαγωγῆς. On this account Aristotle has 
not explained the theory of Induction as thoroughly as that 
of Syllogism. He believes that the only scientific Induction 
is the perfect (cf. $ 128):° δεῖ δὲ νοεῖν τὸ I’ τὸ ἐξ ἁπάντων τῶν 
καθ᾽ ἕκαστον συγκείμενον" ἡ γὰρ ἐπαγωγὴ διὰ πάντων. He 
only says, in his logical writings, of the procedure in imperfect 
induction, that to generalise many experiences of the same 
kind is admissible only when there is no contrary case :® πρὸς 
δὲ τὸ καθόλου πειρατέον ἔνστασιν φέρειν " τὸ γὰρ ἄνευ évoTdcews, 
ἢ οὔσης ἢ δοκούσης, κωλύειν τὸν λόγον δυσχεραίνειν ἐστίν. εἰ οὖν 
ἐπὶ πολλῶν φαινομένων μὴ δίδωσι τὸ καθόλου μὴ ἔχων ἔνστασιι", 
φανερὸν ὅτι δυσκολαίνει. The thought that causal connection 
enables us to generalise is in Aristotle the ruling one in the 
construction of definite inductions,’ but does not attain to a 
fundamental significance in his logical theory. 

Following Aristotle, Boéthius defines :® inductio est oratio, 


I Anal. Post. i. 18. 

* E.g. in the assertion quoted in § 12, from Metaph. xiii. 4, that 
Socrates was the author of Induction and Definition. 

3 Anal. Post. i, 18. 4 Anal. Pri. ii. 98. 

° Anal. Pri. ii. 23. 6 Top. vii. 8. 

7 De Partibus Animalium, iv. 2, 667 a, 37; longevity of animals 
which have no gall. 

® De Differentiis Topicis, oper. ed. Basil. 1546, p. 864. 


. 








480 $ 127. /nduction in General. 








per quam fit a particularibus ad universalia progressio (Syl- 
logism, on the other hand, deduces ab universalibus in par- 
ticularia). It was reserved for modern times to bring out the 
full significance of inductive procedure. In the Middle Ages 
the favourite method of procedure was the deduction of the 
individual from given principles. In modern times men have 
sought to find out the principles themselves in a scientific way, 
and for this purpose required induction. Modern investigators 
of nature use the inductive method along with mathematical 
induction, and Bacon of Verulam outlined the fundamental 
features of the theory itself. He wished to get at a more 
methodical procedure than the simple enumeration of individual 
cases, which may be always contradicted by other cases. 
Bacon says:! Inductio quae procedit per enumerationem 
simplicem, res puerilis est et precario concludit et periculo 
exponitur ab instantia contradictoria et plerumque secundum 
pauciora quam par est et ex iis tantummodo quae praesto sunt 
pronunciat. At inductio quae ad inventionem et demonstra- 
tionem scientiarum et artium erit utilis, naturam separare debet 
per reiectiones et exclusiones debitas.ac deinde post negativas 
tot quot sufficiunt super affirmativas concludere, quod adhue 
factum non est nec tentatum certe nisi tantummodo a Platone, 
qui ad excutiendas definitiones et ideas hac certe forma induc- 
tionis aliquatenus utitur. He seeks to define the correct 
method of procedure more nearly (although in an insufficient 
way). 

The dogmatic course of development of later philosophy 
from Des Cartes to Leibniz and Wolff did not despise Induc- 


tion, but did not advance its theory beyond the doctrines of 


Aristotle. It had more interest in Deduction. 
Wolff, however,? correctly hints that causal connection 
enables us to form universal judgments out of individual ex- 


periences. He does not give to this procedure the name οἱ 


imperfect Induction (§ 129), because the reproach of unscien- 
tific character still clung to the external apprehension of ın- 
ductive method, but opposes it to induction as a better pro- 


cedure. 


1 Nov. Org. i. 108. 2 Log. §§ 706-708. 


§ 128. Perfect Induction. 481 





The empirical tendency for which Locke prepared the way 
favoured Induction, but, because it turned too much aside from 
all metaphysical relations, was not able to do much to essen- 
tially enrich or deepen the theory of this method. 

The latest attempts to carry out what Bacon purposed in 
his Novum Organum, by aid of the scientific means of our 
time, and in a way corresponding to the present stand-point of 
the positive sciences, have mostly proceeded from philosophi- 
cally-inclined cultivators of natural science. Besides the works 
(mentioned in ὃ 35) of Whewell, J. Herschel, J. S. Mill, and 
A. Comte, we must here notice the treatise of Apelt, proceeding 
upon the philosophical fundamental axioms of Kant and Fries: 
Die Theorie der Induction, 1854. Oesterlen has much that is 
valuable, more particularly with reference to his special pro- 
vince, in his work, Médicinische Logik, 1852. Cf. also Liebig, 
Induction and Deduction (speech delivered in the public 
session of the Academy of. Sciences at Munich on March 
28, 1865), who does not sufficiently separate the logical 
form of Induction from the happy anticipation of scientific re- 
sults attained by the power of the imagination of the practised 
investigation familiar with the object. [Cf. also in the same 
em Prof. Tyndall: On the Scientific Use ofthe Imagina- 
10n. 

Upon the inductive methods of investigation (in the wider 
sense of this expression ), cf. § 140. 


§ 128. Perrecr Inpuction (Inductio Completa) is 
that in which the sphere of the subject in the minor 
premise falls wholly and completely within the sphere 
of the predicate. This takes place when, by a per- 
fect enumeration of all individuals or particulars, the 
whole sphere of the universal is exhausted. (By com- 
plete enumeration of all M,, M,, M, : . the whole 
sphere of S is exhausted.) Accordingly in this case the 

II 





u 
= 


x: 


δοῦλα 


τ τι nr rn pete» 
a an Fi 


τῳ “ὼς 





482 § 128. Perfect Induction. 

















minor premise may be brought by conversion to the 


disjunctive form— 
Every S is either M,orM,.. 


. or M,. 


In this way the inference passes over into a conjunctive- 
disjunctive syllogism of the First Figure, and is to be 
proved, according to the general rules of the syllogism, 
from the relation of its spheres. Every 8 falls within 
a sphere, and the whole sphere of all S coincides with a 
sphere which itself falls within the sphere of P. Hence 
every Κα is P. 

Perfect Induction with an infinite enumeration of 
parts is possible in two cases :— 

1. When! the parts are connected together continuously 
in space, so that a survey of all is possible in a finite 
(and often in a very short) time. This happens in every 
geometrical demonstration when the inference, which 
has to do directly with the simple figure it refers to, 1s 
extended and made universally valid for all figures 
falling under the like definition. 

2. When the parts are not continuously connected, 
if it can be syllogistically proved that what is true of a 
definite n™ part must also be true for the (n+1)™ part. 
This last method, however, which mostly finds applice- 
tion in Arithmetic, is not purely inductive. 


In Perfect Induction the sphere of what has the predicate 


P, according to the major premise, coincides with what has the 


predicate P according to the conclusion. Hence this mode 0! 
inference comes within the general notions of Inference and In- 
duction only in so far as it is seen to be an extreme case, Just 4s 


the universal is comprehended under the particular as an extreme 


1 As Beneke remarks, Log. ii. 52 ff. 


$ 129. /mperfect Induction. 483 








case. So long as the series in the enumeration of the indivi 
duals or classes M,, M,... . is not completed, the s μὸν 
of S is wider than the sphere of M,,M,. . and re ἐς 
ference results in something more ne The ἀπ πῆ 
ey oe of the sphere of the subject, or Hemet 
ie predicate, leads up to an equality of spheres, never 
The following are examples of Perfect Induction :— 
Mercury revolves on its axis; So do Venus the Eartl 
Mars, Jupiter, and Saturn. But these are all FR old plan a 
Therefore the whole of the old planets revolve upon diate = 
The angle at the circumference of a circle is half the sen ὦ 
the angle at the centre on the same arc, when the cer = of 
the circle is within the angle at the circumference a 
in one of its sides, and when it is outside of it. But th z 
three positions are the only ones possible: Therefore the a er 
at the circumference is always half the size of th N in 
centre on the same arc. ων 


§ 129. Imrerrect Inpuction (inductio incompleta) 
warrants a particular conclusion only according to 
syllogistic rules: At least some S is P; at least ER 
thing which is both o,, o, . - is P. The conclusion 
ne with more or less probability, and the 
lank which remains over i 
spheres is legitimately Alled ti nen napa ᾿ 

| I 7) partly on the universal 
presupposition of a causal-nexus in the objects of know- 
ledge, partly on the particular presupposition that in 
the case presented such a causal-nexus exists as con- 
nects the subject and predicate of the conclusion. The 
degree of probability of the inductive inference depends 
ἴῃ each case on the admissibility of this last st ee 
tion, and the various inductive operations, the Be 


of the spher | 1 
the sphere of observation, the simplification of the 
iz2 








484 $ 129. /mperfect Induction. 





observed conditions by successive exhaustion of the 
unessential, &c., all tend to secure its admissibility. 

A fact which establishes an objection against the 
universal validity of the inference is called an Jnstance 


(instantia, ἔντασις). 

The first example in the preceding paragraph (of Perfect 
Induction) becomes an Imperfect Induction, when either the 
revolution upon the axis has been observed of some only of 
the bodies called planets (Mercury, Venus, the Earth, Mars, 
Jupiter, Saturn), or when, on the other hand, while the given 
results of observation of all serve as a starting-point, the 
inference is extended to the whole of the planets (not merely 
to those called the old planets). The universal conclusion is 
made probable by the presupposition, that the earth revolves 
on its axis not because it is the earth, i.e. because it is this 
definite planet, and Mars not because it is Mars, not because of 
its proper qualities, but that every one of these planets revolves 
on its axis, because it is a planet, because of its planetary nature. 
There is a certain causal-nexus existing between the nature 
of a planet and (at least the present) revolution upon the 
axis (which may be founded upon the original nature of the 
planet). The multitude of observed cases leads us to assert 
that this relation exists. If it were possible, on the basis of a 
single observation, to know on what causal relation this was 
dependent, we would not need more cases to establish the 
induetive connection. If it were possible to know by a single 
observation whether the earth revolves on its axis or is in- 
habited, &c. because it is a planet, or because it is this planet, 
because of its universal, or because of its individual nature ;— 
whether a stone falls because it is a dense body belonging to 
the earth, or because it is matter ;—whether iron, lead, gold, 
&e. are heavier than water because they are metals (in which 
case the metals Sodium and Potassium must be heavier than 
water, while they are lighter);—whether a medicine heals 
because of the generic or the specific nature of the medicine 
used, and of the disease treated, or because of individual and 


$ 129. /mperfect Induction. 485 





accidental circumstances ;—whether the rose which we see has 
white blossom, has it because it is a rose, &c.;—we would 
not need to bring in other cases into our induction. We are 
inclined to come to a decision upon this point after a single, or 
a few observations, but the primitive inductions thus formed 
are mostly false. The certain scientific knowledge which recog- 
nises whether the judgment forming a ground of the induction 
contains a predicate which belongs to the subject because of 
its generic nature, because of its individual nature, or because 
of accidental circumstances, is not the point from which Induc- 
tion starts, but its essential aim. Among the many primary 
inductions, most of which further experience rejects, there are 
some which are never rejected. These concern the elementary 
relations which have an essential causal character. They form 
the standard by which all other inductions are to be tested. 
The sciences of organic nature have become enlarged by 
inductively making universal the individual results of observa- 
tion. The sciences of inorganic nature rest more upon the 
combination of induction with deductions deduced by the aid 
of mathematics. The same principles of method find applica- 
tion within the province of mental life. We limit ourselves 
here to the universal elements of the thecry of induction, and 
refer to the well-known works of Whewell, Mill, Apelt, 
Vesterlen, and others, for its particular applications in the 
individual sciences. | 
The significance of Induction as a mean to expand our 

knowledge rests upon the same reference to a real conforma- 
bility to law (according to the axiom of Sufficient Reason, 

§ 81), on which the possibility of the syllogism as a form of 
knowledge is founded. It is a mere prejudice which places 

the one of these forms before the other in scientific value, 

whether the syllogistic procedure is thought exclusively 

capable to demonstrate, or whether, on the other side, Induc- 

tion only is thought able to advance knowledge, and Syllo- 

gism to serve merely for the arrangement, explanation, and 

communication of knowledge already possessed. Propositions 
which are absolutely highest, and so cannot be syllogistically 





~ 
Sa Eee 


eu Be 
u N 


« «»΄...... 
-“ 


u... 


- 








486 δ 129. Lmperfect Induction. 





deduced, so far as they are neither identical nor analytically 
formed judgments, can only be scientifically established by 
Induction. 

Inductive inference has strict universality when S con- 
tains the ‘sufficient reason’ of P, when P is related to S 
as its only possible cause or conditio sine qua non, and, lastly, 
when S and P are both necessary consequences of a common 
cause, sufficient for P and the only possible cause of S. On the 
other hand, Induction leads only to comparative universality, 
or to rules which may be limited by exceptions, when S is only 
a single co-operative cause or condition of P, or when, on the 
other hand, P is not the only possible cause of S, or when § 
and P are consequences of a common cause but may also 
result singly under different conditions. Lastly, inductive 
inference is altogether untenable when no causal-nexus of any 
kind can be supposed to exist between S and P. 

The correct formation of notions (cf. § 66) is conditioned 
by the correct formation of judgments and inferences; and 
the latter by the former. The formation of valid inductions 
especially is very closely related to the formation of notions 
according to their truly essential attributes. The possibility 
of correct inductive generalisations depends upon a good 
formation of notions. For a great number of properties and 


relations stand in a causal-nexus, on which the validity of 


the Induction depends, with the essential attributes of the 
object of which (according to $ 56) the notion is formed. From 
this comes the logical right to refer properties inductively to 
the whole species, which have been observed in single indivi- 
duals of a species, in so far as they are not evidently con- 
ditioned by mere individual relations. Contrary cases always 
remain possible, however, so long as the kind of causal con- 
nection is not clearly known. 

The axiom of inductive generalisation which Newton enun- 


ciates! with immediate reference to the physical properties οἱ 


bodies :—qualitates corporum, quae intendi et remitti neque- 
unt, quaeque corporibus omnibus competunt, in quibus ex- 


1 Princip. Phil. Nat. bk. iii. 


N 129. /mperfect Induction. 487 





perimenta instituere licet, pro qualitatibus corporum univer- 
sorum habendae sunt, may be traced back to the presupposition 
of an internal connexion of such properties with the essence of 
the bodies. 

Since syllogistic procedure is synthetic, the inductive, 
in so far as it separates the given object into its partly 
common, partly special elements, may be called analytic. 
We cannot agree to the opposition enunciated by Trendelen- 
burg' between Induction and the Analytic procedure, accord- 
ing to which the former only sums up the fact of the universal 
from the individuals, while the latter seeks the universal 
cause from the given phenomenon, for the reasons we have 
stated ($ 101) when opposing the analogous separation 
of syllogism and synthesis. Trendelenburg’s so-called ‘ ana- 
lytical procedure’ must take the inductive form, and scien- 
tific induction the ‘analytical’ element which refers to the 
causal-nexus. Hence, every such distinction only corre- 
sponds to that of the ‘ formal’ and ‘ real’ sides of Induction. 

The distinction between Induction and Abstraction lies in 
this, that the former has to do with the universal proposition, 
and the latter with the universal notivn. This specific dis- 
tinction cannot be said to be one of degree only ?—Induction 
leading to universal theorems, and Abstraction to necessary 
and fundamental truths. There are not two kinds of universal 
conceptions (as Apelt asserts),? notions and laws; for the law 
is not.a conception, but is the constant way in which some- 
thing actually happens, and our consciousness of it is a judg- 
ment or combination of conceptions, in which that constancy 
is thought to be'real. The real nexus of things conformably 
to law may be recognised either deductively i.e. syllogis- 
tically, or inductively, never 4 priori in the sense of Kant, 
Krause, Fries, and Apelt—not even in Mathematics. Mathe- 
matics is certainly not an inductive and empirical science in 
the sense that its individual theorems must be established by 


' Log. Unters. 2nd ed. ii. 282; 3rd ed. ii. 315. 


As Apelt does, Theorie der Induction, p. 54 ff., Leipz. 1854. 
P. 56. 





488 δ 129. /mperfect Induction. 





the method of empirical observation and measurement; they 
are syllogistically proved, and their free combination goes far 
beyond the forms empirically given: but the certainty of 
those mathematical fundamental propositions which are syn- 
thetical judgments, and especially of the geometrical axioms, is 
based upon empirical observation and induction. In 80 far as 
this observation and induction do not warrant their ab- 
solutely strict and universal validity, what is lacking is supplied 
hypothetically (as Dugald Stewart showed) by means of ideal- 
ising what is given,’ and these hypothetical elements attain 
scientific certainty in the way that all hypotheses do,—by the 
agreement of their consequences, of the innumerable individual 
theorems which are syllogistically inferred from them, with 
each other, and with what is empirically given, which agree- 
ment results more and more in every attempt, the more strictly 
we construct the figures. When this agreement has been 
tested often enough to exclude the possibility of a mistake in 
the principles of demonstration, the certainty of the result in 


every new deduction is secured before the experience specially 


directed to it, or relatively a priori. 

The Kantian doctrine of the absolute a priority of the in- 
tuition of space would not, even if it were correct, ensure the 
necessary truth of the defined individual axioms. That doc- 
trine, however, is only an attempt, which has miscarried, to 
explain the mathematical certainty actually existing, and has 
its stronghold not in immediate experience, but in the systematic 
concatenation of propositions attached to this experience. This 
systematic concatenation does not create the geometrical order, 
but reproduces and reconstructs for our consciousness the real 
relations which lie essentially in nature itself. Kant hypos- 
tatises the formative activity of the mind operating according 
to logical laws conditioned by forms of existence into a product 
called form—into the presumptive intuition of space existing ἃ 


1 This does not presuppose ideal pictures ready in human mind 
which exist previous to all experience, any more than artistic idealisa- 
tion presupposes ideal forms existing originally in the mind ; it follows 
the hint given by the objects. 


$ 129. Lmperfect Induction. 489 





priori, and reduces the apodicticity which belongs to the 
whole of mathematical thinking in its relation to what is 
actually given, to the presumptive distinctive origin of the 
mathematical fundamental intuitions, just as is done in other 
departments of thought by the doctrine of innate ideas.! 

Hegel’ recognises Induction and Analogy to be the bases of 
Syllogistic Inference, because the major premise depends upon 
those forms. This is true of Induction, and also of Analogy, 
in so far as an inference of induction is contained in it (ef. § 131). 

Trendelenburg® opposes the following question to Hegel’s 
opinion: Have the necessary primary judgments of Geometry, 
which form the basis of a series of inferences, become what they 
are from Induction or Analogy? This question, when strictly 
defined as we have done it, is decidedly to be answered in the 
affirmative. They have been made foundations of mathematical 
inference by Induction, aided by Abstraction, Construction, 
and Idealisation. Their scientific certainty, however, does not 
depend upon Induction alone. It depends more on the fact 
that the propositions derived from them syllogistically with- 
out exception agree with each other and with experience, for 
the smallest mistake lurking in the fundamental axiom would 
be increased in these propositions so that it would be sure to be 
observed. 

Schleiermacher says'—* The possibility of the original acts in 
the process of Deduction lies in a reference back to the original 
acts in the process of Induction :”5 “as in the first and second 
original moment the process of Deduction must be referred back 
generally to the process of Induction.’ He is right when he 
enunciates the canon in its universality without exception. 

Leopold George explains in his Logic the doctrine of science,® 


' Cf. Plat. De Rep. vii. 533; Aristot. Anal. Post. i. 18; J. Her- 
schel, A Prelim. Disc. p. 95 ff.; 5. 8. Mill, System of Logic, 7th ed. i. 
204 ἢ; Beneke, Log. i. 73, ii. 8, 51,.86, 151 ff; Drobisch, Pref. to 
2nd ed. Ρ. vi. ff. 

᾿ Eneyel.$ 190. 3. Log. Unters. 2nd ed. ii. 342; 3rd ed. ii. 376. 

* Dial. § 279. > Ibid. § 238. 


6 “7. γε 1 
= Logik als Wissenschaftslehre, Berl. 1868, ‘ dedicated to the manes 
of Schleiermacher,’ 





z= = - —- . .- = > = > = 
ΡΜ Ψ EN Ss TAS ae ee Κ 


490 § 130. Zhe most Notable Errors in Induction. 








and declares that the reference of Induction to the objective 
causal-nexus is a circle, since the knowledge of the real nexus is 
always based upon incomplete inductions. But this objection 
rests upon a confusion of the existence of the causal-nexus and 
our knowledge of it. Its existence precedes our inductions, 
but our knowledge of it in a universal form results after a mul- 
tiplicity of special inductions. We generalise at first only 
according to mental (psychic) laws of association ; our general- 
isations have logical correctness in so far as they each time 
correspond to the objective causal-nexus, and the inductive 
methods are really the means of attaining to this correspon- 
dence. The highest induction is that by which we recognise 
the universal validity of the law of Causality itself. 

The question, in how far the inductive knowledge presupposes 
mental (geistige) self-activity and forms, which are brought 
from what is within to apprehend what is without, has been sub- 
jected to strict investigation by Beneke.' [This question lies 
at the basis of the differences of views held by Whewell and 
Mill regarding the nature and aim of scientific methods. 
Whewell attributes more to the speculative power of the in- 
dividual investigator, and seems to consider that the chief part 
of scientific method is the construction and testing of hypothe- 
ses, and their gradual conversion into scientific conceptions. | 


§ 130. The most common FALLACY against the laws 
of Induction is that of false generalisation (fallacia fictae 
universalitatis). This fallacy generally arises either 
from the confusion of an Imperfect with a Perfect 
Induction, or from the false presupposition of a strict 
causal-nexus from subject to predicate of the conclusion 
(non causa ut causa, sive post hoc ergo propter hoc). 


For example, when the rules for the calculation with powers 
are proved in all those relations which subsist along with 
positive whole exponents, and these rules without further de- 


1 Syst. der Logik, ii. 23 ff. 


§ 131. /nference by Analogy. 491 





monstration are taken quite universally, and as valid in powers 
with negative fractional and irrational exponents,—this is a 
case, so far as the method is concerned, of incorrect generalisa- 
tion (although as a matter of fact it is not false) or of false 
resting upon an I/mperfect Induction while the Perfect is re- 
quired and is attainable. 

The most numerous and most important examples of false 
Inductions which depend upon ignorance of the true causal- 
nexus, and the imaginary substitution of a supposititious one, 
are afforded by superstition in the inexhaustible multiplicity 
of its forms, which, dragged from its thousand hiding-places, 
always burrows in new ones. The history of serious investi- 
gation, however, makes it evident, in the many errors of 
this kind of which it has to report,! that man must find scien- 
é 
tific truth, the highest point he can reach, as well as moral 
sentiment, not ready made like a gift without effort on his part, 
] Y 52 r 
ut only by long and hard struggle by way of development, 
and especially by overcoming his natural propensity to a false 
anthropomorphism. 

In many cases the wage of language, not yet corrected by 
science, leads to false inductions. The sphere of the concep- 
tion, to which the word refers, does not necessarily coincide 
with the spheres of those notions, to whose objects the predicate 
in question belongs. The variety of connected circumstances 
18 § si r . - . 

not easily detected by the superficial glance, and we are apt to 
attribute the same predicate to all that we denote by the same 
name, until we have learned to subject to logical laws the psy- 
chological association of conceptions which the word suggests.” 

Ἢ ᾿ . A:17 . 5 » . © 
| The ee in Mill’s Logic on fallacies of generalisation 
contains* a series of examples of false inductive inferences. 


N "ὦ Ξ 
§ 151. The InrerencE or ANALocy (exemplum, 


analogia, mapdds fa) is 
gla, παράδειγμα, ἀναλογία) is an inference from 


Irre r 9 ᾿ 
u Whewell’s important work, The History of the Inductive 
ICU nces, 1859-42. 


2 Of aa ’ u i 
Cf. Beneke, System der Logik, ii. 59 ff. > 7th ed. u: 352, 








§ 131. /nference by Analogy. 





particulars or individuals to a co-ordinate particular or 
individual. Its Schema is the following :— 
a Es 
S is similar to M 


5 = # 


Or more definitely, since it also gives that in which 
the similarity consists, the following :— 
M is P 
em Ss 
> m & 
3 ἃ Ὁ 
Sometimes the notion M, sometimes the notion 4, 
sometimes both of the two notions are plural. Hence 
three forms arise, the first of which corresponds to the 
fundamental form of the Inductive Inference, the second 
and the third to the secondary forms mentioned above 
(ὃ 127). Every inference of Analogy may be resolved 
into an Inductive Inference of the corresponding form 








and a Syllogism. 
The First form of the Inference of Analogy, stated 


more particularly, is the following :— 
M,, as well as M,, and M,.....is P 
M,, as well as M,, and M,..... is A 
> ἃ ἃ 
Ss = Ὁ 
This is reduced to the Inductive Inference of the first 


form— 


M,, as well as M,, and M,.....is P 
M,; as well as M,, and M,.....is A 


» ae 








§ 131. /nference by Analogy. 493 








and to the corresponding syllogism of the First Figure—. 
m ἜΣ. 
D is A 
= m 
The Second form of the Inference of Analogy is the 
following :— 
ie FF 
M is A,, as well as A,, and A, . 
S 18 A, as well as A,, and A, . 


S is P 





This form reduces itself to the inference— 
M is P 


M is A, as well as A,, and A, . 





Whatever is A,, as well as ἃ. and a4, ..... is ἢ 


and to the corresponding syllogism in the First Figure— 
T . 
Whatever is A,, as well as a,, and a,..... is P 
Sis A,, as well as A,, and A, . 


> << Ἢ 


The Third form of the Inference from Analogy com- 
bines the peculiarities of the first two— 


M,, aa wellasM,.....iP 
M,, as well as M, . 








. is also A, and A, . 





S is pP 


When r y 7 ine j 
resolved the two following inferences result :— 


M,, as wellas M,..... is P 


\ M . 
I, as well as M,, . is also A, and A, . 








Whatever is a, and a,..... is P 








ee ee 


ἱ 
" ᾿ 
tt 
Mi 
i} 
" 
i 
‘} 
ἢ Ν 
δ 
ΠΝ 
Hk 
wg i j 
A. 
Mi 


494 § 131. /nference by Analogy. 





and— | 
Whatever is both A, and A,.....isP 
S is both A, and A ..... 


is P 


These three forms of the syllogism of Analogy may 
also occur with hypothetical premises. 





The following is an example of an inference of Analogy of 
the first form :— 

Mercury, Venus, the Earth, Mars, Jupiter, and Saturn (the 
whole of the planets known to the anciénts) revolve on their 
axes from west to east; all these are planets of our system; 
Uranus also belongs to planets of this system: Hence it pro- 
bably revolves on its axis from west to east. 

The following is an inference of Analogy of the second form:— 

The Earth supports organic life; the Earth is a planet re- 
volving in an orbit round our sun, turning on its axis, having 
an atmosphere, the change of seasons, &c.; Mars 15 a planet 
revolving in an orbit round our sun, turning on its own axis, 
having an atmosphere, the change of seasons, &c.: Hence 
Mars also will probably support organic life. | 

Of the same form is the inference which Franklin made in 
November, 1749,! and which must be reckoned among in- 

iti ibsumption 
ferences of Analogy on the presupposition that the = I | 
i i 1 y men: 
of the notion of lightning under that of electrical p einer 
was not yet made, and the two notions were only thought 
similar: The electric fluid, as it shows itself in experiments 
made by us, is attracted by projecting metallic points; = 
-operti at they 
electric fluid and lightning agree in the properties that the: 
ceive light of the same colour, have a quick motion, are con- 
= > - . fi ‘ 
ducted by metals, &c. &c.: Hence it is to be presumed that 
lightning will also be attracted by projecting metallic pomts. 
oO 


The example quoted of an inference of Analogy of the first 


i : : ity οἱ 
form passes over into the third form, when pee avant, | 
nature which Uranus has with the old planets is denoted no 


1 Cf. Beneke, Zog. ii. 119. 





δ 131. Luference by Analogy. 495 


only by the general nature of planet, but also by the particular 
quality by which all these planets (together with N eptune) 
are distinguished from the asteroids, viz. that they are larger 
and the only planets which are always ata defined distance from 
the sun. 

There are not two kinds of Inference by Analogy, the Per- 
fect and the Imperfect, according as the Induction implicitly 
contained in it is of the one kind or the other; for if the 
Induction is Perfect, the case which is first inferred by Analogy 
must be given as a premise. Hence the Inference by Analogy 
can only be joined to an Imperfect Induction. All forms of 
Analogy are distinguished from induction by the adjoined 
syllogism, which concludes from the universal reached by pre- 
sumption to the particulars or individuals. 

The certainty or probability of the inference by Analogy is 
founded on the same moments as that of the Imperfect Induc- 
tion. It depends on the correctness of the presupposition of a 
real nexus conformable to law between A and P. For the 
reference to single analogous cases must be true in the very 
same measure and from the same reasens as the inductive 
generalisation. No new uncertainty enters in its syllogistic 
subsumption under the universal law for the present held to 
be valid, and the reference to the single analogous case is 
justified only in so far as a universal conformability to law is 
presupposed, according to which the same predicate can also 
be added inductively to all those objects which strictly cor- 
respond to the same conditions. 

The fallacies which appear in Analogy, because it is a com- 
bination of Induction and Syllogism, are the same as those 
which enter into those modes of inference. They depend for 
the most part on the false presupposition that the predicate P 
belongs to M because of its universal nature A, and therefore 
will belong to other a, and to 5, while P really belongs to 
the specific difference of M which S does not share with it. 
So long as a connection conformable to law cannot be pre- 
Supposed between a and P, the proposition holds good: idlus- 
trations and parables prove nothing. 








u andern! 





496 δ 131. /nference by Analogy. 





Examples of false inferences from Analogy lie in the old 
belief of the animate nature of the heavenly bodies from the 
analogy of men and animals because they were moving beings. 
(Cf. § 42.) By a very doubtful analogy the persistence of 
mental (psychic) impressions was made parallel with the per- 
sistence of a body in a state of rest or motion, according to 
the law of inertia.! Mill gives other examples.’ 

Analogy is related to Proportion, but not identical with it. 
If we call the P which belongs to M, P’, and the P which 
belongs to S, P”, the Inference from Analogy may be reduced 
to the following formulas :— 

oe 94 50 


or 


MB: =3 : ἘΠ 


In the latter form the A may be reckoned the exponent. But 
in most cases this representation is only an illustration, and is 
not exactly true. But the cases in which it is exactly true 
(as in the so-called ‘Rule of Three’) do not lead only to the 


inference S is P, but also to the nearer determination of Pas 
P” (e.g. not merely to the inference that the second quantity 
of goods has a value, but also to the calculation of this value); 
for the predicate P does not belong to the two subjects M and 
S, only in so far as its class-nature A goes, but is also modified 
according to the relation of their specific peculiarities (M and 
S). An inference of this kind may be called the Inference of 
Strict Analogy * (as Drobisch does, Log. 3rd ed. § 149). 

The first of the examples of the Second form of Analogy, 
reduced to the form of Proportion, would run: As the Earth 
is to Mars, so is the organic life on the earth to the (pre- 
supposed) organic life in Mars; or: as the Earth is to its 
organisms (exponent: planetary nature), so 18 Mars to its 
organisms (exponent: planetary nature). 

Aristotle‘ distinguishes the Inference from Analogy (παρά- 
Sevyua) on the one hand from Induction, and on the other from 
Syllogism, in this way, that conclusion is made neither from the 
2 Logic, 7th ed. ii. 362. 


1 Cf. Lotze, Mikrokosmos, 1. 214. 
4 Anal. Pri. ii. 24. 


3 Analogia Exacta. 


§ 131. /nference by Analogy. 497 





part to the whole, nor from the whole to the part, but from 
the part to the part. He resolves Inference by Analogy into 
an inference to the more universal (which is an ἜΘΝΗ 
of Imperfect Induction, although Aristotle does not use this 
term, because he recognises Perfect Induction only; cf. § 187) 
and an adjoined syllogism :! φανερὸν οὖν ὅτι τὸ παράδειγμά 
ἐστιν οὔτε ὧς μέρος πρὸς ὅλον, οὔτε ὡς ὅλον πρὸς HEP9S, ἀλλ᾽ ὡς 
μέρος (A) πρὸς μέρος (T'), ὅταν ἄμφω μὲν ἢ ὑπὸ ταὐτὸ (Β) yvo- 
ριμον δὲ θάτερον (A, scil. örı τὸ A αὐτῷ ὑπάρχει). καὶ RER 
τῆ» ἐπαγωγῆϑ, ὅτε ἡ μὲν ἐξ ἁπάντων τῶν ἀτόμων τὸ ἄκρον 
ἐδείκνυεν ὑπάρχειν τῷ μέσῳ καὶ πρὸς τὸ ἄκρον οὐ συνῆπτε τὸν 
συλλογισμόν, τὸ δὲ καὶ συνάπτει καὶ οὐκ ἐξ ἁπάντων δείκνυσιν.3 
He gives the following example: ἔστω τὸ A κακὸν, τὸ δὲ B 
πρὸς ὁμόρους ἀναιρεῖσθαι πόλεμον, ἐφ᾽ ᾧ δὲ Γ' τὸ Ἀθηναίους πρὸς 
Θηβαίου», τὸ δὲ ἐφ᾽ ᾧ Δ Θηβαίους πρὸς Φωκεῖς. He deduces 
from the empirically given case that the war made by the 
Thebans against the Phocians was destructive (A is A), by 
the Imperfect Induction, that, because that war was a war 
against neighbours (A is B), every war against neighbours is 
destructive (Bis A). It is then inferred syllogistically that a 
war of the Athenians against the Thebans (I), because this 
would be a war against neighbours (Τ' is B), would be destruc- 
tive (is A). Hence the three premises are given :— 

. Em 3 

> AS DB 

ἃ, © =; 5 


A ‘ls ᾿ς 1 
rıstotle first deduces presumptively from 1 and 2— 
 B = A, 
and after this is ‘ > 
1 ter this is shown (ὅταν τῷ μέσῳ, sc. τῷ B, τὸ ἄκρον SC. TO 
A, ὑπ n διὰ Do 5 Δ εν 
τ ἫΝ δειχθῇ διὰ τοῦ ὁμοίου, sc. τοῦ A, τῷ τρίτῳ, SC. τῷ 
)» he lastly isti 
y deduces syllogistically from 4 and 3 the result— 
a FF we A, 
From tl i 
| ıese two consequences which are contained in the one 


inference fr ; 
crence from Analogy, the first is that one on which the final 
' Anal. Pri. ii. 24. 2 Cf. Rhet. i. 2. 


K K 











§ 131. Lnference by Analogy. 


498 








decision depends, since the validity of the whole stands and 
falls with its validity; the second, or the syllogism, con- 
cludes easily and undoubtedly. Aristotle, therefore, bestows 
special attention upon the first element of Analogy, and 
explains it to be a kinu of Induction which is imperfect, 
and more rhetorical than scientific, because what is the more 
universal is not proved from an exhaustive enumeration 
of every individual case, but from one or a few individual 
cases. Analogy is related to Induction as the Enthymeme is 
to Syllogism:! as δ᾽ αὔτως“ καὶ οἱ ῥητορικοὶ συμπείθουσιν " ἢ γὰρ 
διὰ παραδειγμάτων, ὅ ἐστιν ἐπαγωγὴ, ἢ δι’ ἐνθυμημάτων, ὅπερ 
ἐστὶ συλλογισμὸς. Aristotle does not ‘use the term ἀναλογία 
with a logical meaning of Analogy, but in the sense of mathe- 


matical Proportion. Theophrastus employs the word in a 
ation, but in one quite different from what it 
He calls thoroughly hypothetical inferences 
2 On the other hand, the term: 
is used of inferences from 


logical signific 
now denotes. 
συλλογισμοὺς κατ᾽ ἀναλογίαν. 

e \ A > 4 ’ 
οἱ κατὰ τὸ ἀνάλογον συλλογισμοί; 


Analogy, and the Schema of mathematical proportion in the 
Tarnvod Εἰσαγωγὴ διαλεκτική ὃ 18 applied.‘ 

Boétthius,> strictly agreeing with Aristotle, teaches: 
propositum parlı- 
oportet ἃ 


Est 


enim exemplum, quod per particulare 
culare quoddam contendit ostendere hoc modo: 
Tullio consule necari Catilinam, quum a Scipione Gracchus 
sit interemptus.— Ex parte pars approbatur.— Exemplum in- 


Quae omnia ex syllogismo vires accipiunt. 


ductionis simile. 
sciences has first 


The modern development of the natural 
made evident the full scientific value of Analogy as well as οἱ 


Induction.® 
Kant explains’ Analogy to be the similarity of two quali- 


1 Anal. Post. 1. 1. 2 Cf. § 121. 3 P. 54 566: 

4 Cf. Prantl, Gesch. der Log. i. 608. 

5 Op. p. 864 sqq., ed. Basil. 1546. 

6 Cf. Gruppe, Wendepunct der Philos. 
p. 34 ff., 1831; and Trendelenburg, Log. Unt. 
ii. 378-385. 

7 Krit. der r. Vern. p. 222. 


im neunzehnten Jahrhundert, 
+i, 302-309, 2nd οὐ; 


4 131. ER ὃν Analogy. 499 





tative relation 
ne 0 ᾿ (while mathematical analogy or proportion 

᾿ \ ᾽ . . 

4 - ee arr ae of two relations of size). He allows 
that Analogy,! li ction, is i 

gy,' like Induction, is in a certain degree useful and 
necessary for the purpose of extending the knowl 

experience, but ks th ei 

‚xperiene rank y N 
“x : : s these two forms, which he calls ‘ In- 

erences of the reflective judgment,’ far behind sylloeis 

alone can pretend to tl lh a 
oe Se ıe name “ Inference of Reason.” For? 

every inference of the reason must give necessity: Inducti 
and Analogy are theref wre ehe 

| : alogy are therefore not inferences of reason they are 

only logical pr oti irical 1 

y Ä gical presumptions or empirical inferences:’? “the uni 
vers: rards which i ive j a | : 

: sal ἴον ΠῚ which it (the reflective judgment) advances from 

\ N S = ‘ . ὩΣ Φ . = . 

a“ Ar is omy empirical universality, merely an analogue 
0 ζ | 
the ogical.’ Kant does not seek to make any reference in 

100 . 7 r 2 = 

gic, or anywhere, to the conformability to law in real exist 
νὴ ‘ c - 

= a that ‘ Inference of Reason,’ or Syllogism, so high! 
exalted abov ἼΩΝ 

ὶ : ıbove Induction and Analogy, with the purely nf 
q sal Ξ . εὲ σ΄ . . : 

Dpre .ension, which Kant finds in it, is still less able t] 
those infer Sc j 1 = R 
” ᾿ oe of the judgment to widen our knowledge. It 

ν Y - + . . ; 
er + 7" 5. in the conclusion to a partial repetition of ws we 
already know id j 
= id now and have already said in the major premise. It 

ve 10 Bey . . . . ° 
ee = a principle of scientific certainty, and Kant himself 

akes : 1 
‘ ne on it only the “ analytical’ forms of thought 
vy w Ἵ - 

y which all our knowledge already possessed i ind 
dip Se a y possessed is analysed and 
= ged, onew knowledge attained. Kant will not recoo 

86 ἃ source icti 1 i a 
eg ree Pa apodictic certainty in all methods of logical ei 

dure in ᾿ and i i τ i 
en 2 erence (and in this agrees with the Sceptics, for 
a a theories of those called by him dogmatic ee RETURN 

or ‘ al . . : 
ots ag ıpprehended by him did not satisfy him). On the 
ıy - 3 r 7 ye € . 
- gi = ever, Kant could not but recoenise (in opposi 
O 16 re 1 4 rn = = 
ib € Sceptics) the apodicticity, which he found i 
positive sciences, to be i ee 
a: » a given fact, and the question how 
apodicticity was possible, to be a prob 
Een Ἂ a problem in the theory of 
a τ τ: 5 ἣν ieee these two presuppositions, Kant’s 
owledge, or the ‘Kritik of pure Reason,’ 
3 


Log. N 8 2 +} 
9. 84. Ibid. ὃ 84, Remark 2. 3 Ibid. § 81. 


"8 ' 
or gis ; re 
ἔχον Ὁ. section in the Aritik d. r. Vern. pp. 218-265 
analogies of experience ; - PP- -265, upon the 
xperlence, has not this tendency 


K Kk 2 








500 § 131. /nference by Analogy. 








δ 131. /nference by Analogy. 


which destroyed so many traditional illusions, could not but 
attain to the somewhat mystical character which it indeed 
possessed. Kant sought the basis of scientific certainty, which 
he could not find in logical laws, outside of them in the supposi- 
titious ἃ priori acquired forms of intuition, Categories and Ideas. 
He ascribes to the ‘I’ of the pure apperception, as an original 
act of the spontaneity of every individual, what in truth pro- 
ceeds from the mental co-operation of individuals and nations, 
what is the historical result of the progress of the development of 
mankind in the course of centuries, and could only appear in 
definite historically-conditioned degrees of culture.’ 

As regards its formal side, Kant teaches? that in the in- 
ference from Analogy the judgment concludes from many 
determinations and properties, in which things of one kind 
agree, to the rest of them so far as they belong to a single 


principle, or from partial to total similarity ; while in Induc- of its Ὁ : ἱ ἱ 
s genus or essential determinateness. ‘The earth has 


tion the judgment concludes from many to all things of one PEG RS ; 
® ze gr 3 ; ere inhabitants ; the moon is an earth: Therefore it has inhab; 
kind according to the principle: what belongs to many things ante as ınhabit- 


of one genus belongs to the rest of them. Kant accordingly 
makes the distinction of Analogy from Induction lie in that 
determination which we make the peculiarity of the second 


the particular, or from the particular to the universal. or (in 
combination of those two forms) from the EEE to a τὰ 
ordinate particular ; and the kinds of inference restine τὴν this 
division have since Aristotle’s time taken the names of Sr TI. 
gism, Induction, and Analogy. All other distinctions includ σ 
that founded on whether the inference is made ΗΝ one = 
from several examples of one genus and on the basis of acree- 
ment in one or several characteristics, are of comparativel 
subordinate significance, and are of value only in the en 
division of those kinds of inference into their species or forms 
Hegel! believes that Analogy takes for its abstract scheme 
the Second Aristotelian Figure (the Third in Hecel’s enum 
ration), just as Induction takes the Third (or the eeu 
according to Hegel). The middle term of the Tabs of 
Analogy is an individual, taken in the essential universality 


While Aristotle combines first of all the first two of the 
three premises A is A, A is B, Γ is B, in order by an inference 
from the individual to the general to deduce the proposition : 
Bis A, which then serves, when taken alone with the third for 
the Major Premise of a Syllogism :—Hoyel would CHE 
thesecond and the third premises: A is B, TısB (or in th 
example : the earth is a world, the moon is a world), in ie 
first of all to deduce the proposition : I" is A (the sani Is : 
18}, which then serves, when taken along with the Fur 
ge nn of a Syllogism. The combination of 
ae ite ἐπ B, T is B, only follows the scheme of the 
ae ci istote ian Figure, in so far as the middle notion B is 
+ “ predicate (while it does not follow the law of the syllo- 

Cf J. G. Fichte, Werke, vii. 608. ? Log. § 8400 ew = Sg ee ee be a 

N ART eee : process has not the truth which that Aristotelian 

Artis Logicae Rud. App. pp. 226-228. ] & = onhas. For the subsumption of T under A is incorrect 

Sect dir Log. p: 466. 7 Ibid. p. 436 ff. | ane has an apparent validity by the double sense (as Hegsl 

[Mansel calls this Analogy, Example: cf. Artis Log. Rudi. 5 
pp. 95 ν, 220.] ' Log. ii. 155 ff., 1834 ; Encyel. § 190. 


form of Analogy. 

Several modern logicians, such as Bachmann, [ Hamilton, 
and Mansel,] follow his example. 

Fries δ remarks, in opposition to Kant, that the going back 
from the universal to the rest of the individuals is the sole 
peculiarity of Analogy, and,’ following Aristotle, reduces 
the inference of Analogy to a combination of an Induc- 
tion with a Syllogism.® The chief division of inferences 
must be based in any case on the most essential of all differ- 
ences,—viz. whether conclusion be made from the universal to 

















3 
nn = --- - 


=e "ξ 588 ΞΞΕΣ 





502 § 132. Determination of Degrees of Probability. 





himself proves ') of the notion A (the earth—an earth). The 

Aristotelian reduction, on the other hand, clearly exhibits with 

logical accuracy the essence of the inference of Analogy on its 
oD 


certain and on its doubtful side. 


§ 132. In so far as the nexus conformable to law 
between ὃ and P is unceriain in Imperfect Induction 
or Analogy, the conclusion has only a problematic 
validity. If the reasons for its existence are of more 
weight than the reasons against, the conclusion has 
probability (probabilitas ). If an attempt be mace to 
define more closely the different degrees intermediate 
between the complete certainty of the conclusion and the 
certainty of its contradictory opposite, the term proba- 
bility 15 also used in a wider sense as the common name 
for the whole of these degrees. The degree of proba- 
bility in this sense admits in certain cases of arithmetical 
determination, which may have not only probability τς 
also certainty. When different analogies, some of which 
point to the conclusion and the others to its contra- 
dictory opposite, are in general alike applicrble, ᾿ 
degree of probability may be represented — y 
as a fraction, whose numerator 1s formed by the num er 
of cases for, and its denominator by the mane “ 

‘ases compared. The degree of probability of a ag 
consequence is the relation of the number οἱ cases, 
which in the same circumstances have led to this result, 
with the number of cases compared. The latter num! er 
must be of a considerable size in empirical statistic 
(e.g. in determining the liability to death in saa 
wounds) in order to be able to estimate the degre 


L Log. ii. 197. 


of 


δ 132. Det rmination of Degrees of Probability. 503 





probability. It is a fixed quantity if the possible kinds 
of results (e.g. as in the game of dice) be deduced 
from the nature of the case, and then lead to the most 
certain inferences. So far as the different analogies 
differ in the degree of the possibility of their finding 
application, a mathematical determination of the degree 
of probability is generally impossible. In this case a 
less exact estimation of the degree of probability may 
be arrived at, which can lay claim to probability only, 
not to certainty. This kind of estimation of the degree 
of probability is commonly called the philosophical in 
opposition to the mathematical, but more correctly the 
dynamic, in so far as it depends upon the relative con- 


sideration of the internal force of the causes for and 
against. 


The terms mathematical and philosophical (dynamic) pro- 
bability are not strict enough. It is not the probability but 
the way of estimating its degree that is mathematical (arith- 
metical) or dynamic. 

The degree 1 =? denotes, according to the definition given 
above, complete certainty, for the number of favourable cases 
is equal to the sum total of all the cases. The degree 0=° 
denotes the certainty of the opposite contradictory, because not 
one of all the cases is favourable. The degree 4 denotes that the 
reasons for and against are evenly balanced. The positive 
fractions from 4 to 1 denote probability in the narrower. sense, 
because the cases for are more numerous than the cases 
against. Lastly, the positive fractions from 4 to 0 denote 
improbability in its different degrees. It belongs to Mathe- 
matics, not to Logic, to describe more definitely the calculus 
of probabilities (calculus probabilium). 

[Cf. Mill's Logic, ii. p. 122 ff.; De Morgan’s Formal 
Logic or Calculus of Inference necessary and probable, pp. 
170-210; and Boole’s Laws of Thought, pp. 243 399. ] 




















504 § 133. Material Truth of the Premıses, etc. 





$ 133. In every Inference formally correct and .of 
strict universal validity the material truth of the con- 
clusion follows from the material truth of the premises, 
but not conversely the latter from the former; and the 
material falsehood of at least one of the premises follows 
from the material falsehood of the conclusion, but not 
conversely the latter from the former. A single pre- 
mise, or all of them, may be false and yet the conclusion 
true; but it cannot happen that the premises are all 
true while the conclusion, correctly deduced, is false. 
Only truth can follow from what is true; but truth as 
well as falsehood from what is false. The proof for the 
material truth of the conclusion derived from true pre- 
mises lies in the logical correctness of the derivation; 
for the logical laws of the formation of inference, like 
logical laws in general, are founded on the idea of 
truth (cf. δὲ 3, 75 ff, 101), and a deduction which 
leads to what is false would prove itself to contradict 
the logical laws and so to be incorrect, in opposition to 
the hypothesis. But, if inference from false premises is 
made conformably to the logical laws, it is not necessary 
that what follows must be true or must be false. Various 
relations determine the particular cases. 


In Syllogism the material truth of the inference correctly 
deduced from materially true premises is necessary; but the 
material truth of the conclusion can also coexist along with the 
falsehood of one or both premises. The analogy between 
inference and calculation should not mislead us to believe that 
the conclusion can have material truth only when several ma- 
terial fallacies balance each other in the premises or hypotheses. 
The incorrectness of a premise, e.g. of a major premise in the 
syllogistic mood Barbara, may lie in a false generalisation, 


δ 134. Hypothesis. 505 





while the corresponding particular may be true, and the mate- 
rially true minor premise may seize upon that part to which 
the predicate of the major actually belongs. For example, all 
parallelograms may be inscribed in a circle; all rectangles are 
parallelograms: Therefore all rectangles may be inscribed in a 
circle. In the same way, the minor premise may be false, if it 
subsumes the S under M instead of under M’, and yet the 
conclusion be true, if P belongs to M as well as to M’. For 
example, in the enthymeme, ‘ The sanctity of treaties has no 
religious reference; and therefore is independent of Church 
doctrines, and of the religious differences of peoples.’! Not 
only that which has no religious reference, but that also which 
has no special religious reference, is independent of the religious 
differences of peoples. 

But this possibility to hit at truth accidentally by a formally 
correct deduction from what is false is not to be looked at as a 
proof of the imperfection of the syllogism.? 

Aristotle taught * ἐξ ἀληθῶν μὲν οὐκ ἔστι ψεῦδος συλλογί- 
σασθαι" ἐκ ψευδῶν δ᾽ ἔστιν ἀληθές, πλὴν οὐ διότι, ἀλλ᾽ ὅτι, and 
copiously illustrated the latter relation’ with reference to 
single syllogistic figures. 


§ 184, Hypotuesis is the preliminary admission of 
an uncertain premise, which states what is held to be a 
cause, in order to test it by its consequences. Every 
single consequence which has no material truth, and has 
been derived with formal correctness, proves the false- 
hood of the hypothesis. Every consequence which has 
material truth does not prove the truth of the hypothe- 
sis, but vindicates for it a growing probability, which, in 


cases of corroboration, without exception, approaches to a 
position where the difference from complete certainty 


' Klüber, Völkerrecht, § 143. 
* As Vorländer does, Erkenntnisslehre, p- 160. 
3 Anal. Pri. ii. 2. 


se i.-iv. 











506 δ 134. Hypothests. 








vanishes (like the hyperbola of the Asymptotes). The 
hypothesis is the more improbable in proportion as 
it must be propped up by artificial auxiliary hypotheses 
(hypotheses subsidiariae). It gains in probability by 
simplicity, and harmony or (partial) identity with other 
probable or certain presuppositions (simplex veri sigil- 
lum; causae praeter necessitatem non sunt multipli- 
candae). The content of the hypothesis acquires 
absolute certainty, so far as it succeeds in recognising 
the supposed reason to be the only one possible by 
excluding all others conceivable, or in proving it to 
be the consequence of a truth already established. 

An hypothesis sufficiently confirmed, so far as it lies 
at the basis of a series of inferences as a common major 
premise, establishes a Theory, i.e. the explanation of 


phenomena from their universal laws. 


The formation of hypotheses is a mean to scientific inves- 
tigation as justifiable as indispensable. ‘ The intelligent man 
is not he who avoids hypotheses, but he who asserts the most 
probable, and best knows how to estimate their degree of pro- 
bability. What is called certainty in a law-case is, at bottom, 
only a probability of the hypothesis which refuses to admit the 
possibility of error in the consciousness of the judge.’' Hy- 
potheses are necessary in all sciences, if the knowledge of 
causes is to be reached. Causes as such are not accessible to 
observation, and, therefore, at first can be thought only under 
the form of hypotheses, until, with the advance of the sciences, 
the previously problematic suppositions pass over into know- 
ledge apodictically certain. But to the most ingenious bold- 
ness in the invention of hypotheses there must be united the 
most cautious accuracy in testing them. Scientific hy potheses 


1 A. Lange in the Zeitschrift für Staatsarzneikunde, N. 8.» xi. 1 


138 f., Erlangen, 1858. 


§ 134. Hypothesis. 





are not (as Apelt! expresses himself) ‘ assertions which have 
been floating in the air, and are laid hold of;’ they are the 
results of regular reflection on experiences, and, as ‘premises 
in tentative deductions, form the necessary preliminaries to 
adequate knowledge. 

In the provinces of the knowledge of nature and of mind, 
enquiry, which is still incomplete and unconscious of its limits, 
falls into error when it fancies itself able to distinguish between 
the absolutely certain and the absurd: it easily changes to 
Scepticism or Mysticism when this error disappears. A riper 
enquiry recognises that in all problems where we must proceed 
upon mere observation, and not with mathematical certainty, 
the scientific correctness of distinct hypotheses must be the 
first object of investigation. An essential advance in method 
in this sense was made in Astronomy, when in the Platonic 
School, and especially by Heraklides of Pontus, the question 
to be investigated was not stated in this way,— What positions 
and motions of the heavenly bodies are to be necessarily ac- 
cepted on empirical and speculative grounds ?—but in this,— 
What hypotheses of regular motions, in themselves possible, 
can be formed which agree with the facts of observation, so 
that the phenomena ‘ may be preserved’ (σωθήσεται τὰ φαι- 
voueva)? Heraklides reckons among these hypotheses that 
of the motion of the earth. Unfortunately Aristotle mis- 
understood and destroyed this real advance in method, under 
the influence of his belief in the capacity of the νοῦς to know 
principles immediately ; for he undertook to decide upon the 
facts themselves, partly by a rash and erroneous application of 
speculativ j 
ie gat heey Inia ee bus asda τὰ ἧς 
Se ) g ication of hypo- 
theses oy an appeal to facts, and uses this verification to some 
extent in his scientific thinking. 

The correct construction of hypothesis is a life and death 
rages: a : for it is the science of the principles 
| lences, and requires, more than any 
other, to pass beyond mere experience, and to bring together 


I Theorie der Induct. p. 173. 























508 δ 134. Hypotheses. 





by comparison very different departments of knowledge. 
Whoever denies this must abandon philosophy to mere empi- 
ricism, or consign it to the old road of immediate a priori in- 
telligence, or to that play of paralogisms,—the so-called “ dia- 
lectic method.’ 

Whenever a problem is under consideration, such as the 
Darwinian Origin of Species, the Wolffian hy pothesis of the 
origin of the Homeric Poems, Schleiermacher’s, K. F. Her- 
mann’s, Munk’s, &c. theory of the arrangement of the Platonic 
Dialogues, the various theories of the genesis of the Gospels, 
&c., the most essential condition for carrying on the investiga- 
tion in a genuinely scientific, and, at the same time, the right 
and proper way for man, lies in this,—Let all the opposing 
fundamental opinions be brought under the view of different 
thoroughly testing hypotheses, and do not let the one opinion 
(as too often. happens if it is the traditional one) be treated 
from outset as correct, necessary, sound, and rational, and those 
of opponents considered to be false, arbitrary, unsuitable, or 
foolish. In scientific investigation every belief which passes 
beyond the bounds of the scientific probability to be setahbubee 
is necessarily accompanied by illiberality, injustice, and passion, 
in proportion to the tenacity with which it is maintained ; and 
this tenacity may arise from supposed ethical considerations, 
as happened to Kant to some extent. = | 

In every comprehensive problem of this kind a great ai 
of single circumstances must necessarily be explained. Now, 
the student, whatever stand-point he may take, very seldom 
reaches the unusually favourable position where he 18 able to 
found a proof of the certainty, or even of the superior proba- 
bility, of his view, and of the untenable nature of all opposing 
opinions upon any one of these circumstances which al : 
to be considered. The conviction of the certainty or super! 
probability of an opinion may be scientifically established by : 
few instances, or even by a single instance, as in the case © 
Bacon’s Experimentum Crucis. In all other instances m 
possibility only, or the tenableness of an opinion, 1s the subject 
of investigation, and the removal of objections which seem 1 


N 134. fLypothests. 509 





prove that opinion to be untenable. In this investigation it is 
not only legitimate but advisable to place one’s self at the 
point of view of a given opinion, in order to construct a suit- 
able, complete, and harmonious theory which may embrace all 
the facts of the case without distortion, by gathering together 
admissible conjectures. Two fallacies are easily fallen into. 
The one is, that he who argues in one way may perceive a 
proof for his opinion in the harmony established in this way, 
although this harmony may entirely differ from the thought 
itself, since, so long as this opinion is not absolutely confirmed 
by the arguments in its favour, the possibility of its being con- 
tradicted is always open. The other fallacy, which as frequently 
occurs, is that when an opponent from his stand-point, accord- 
ing to its internal consequences, frames his opinion, and keeps 
himself free from any confusion between argument for the 
possibility, and arguments for the necessity of his view, he is, 
nevertheless, without purely or completely acquiescing in his 
stand-point, argued against as if the necessity of his opinion 
were the matter of investigation in every instance. What is 
uncertain, too, in his statements, which he requires in order to 
thoroughly carry out his fundamental view of the matter, is 
made matter of reproach against him. His presuppositions 
are treated as if they were a mere play of conjecture and 
evasion, an inadmissible departure from the ground of fact, a 
creation of hypotheses from hypotheses, reasoning in a circle, 
or, at least, a capricious acceptance of what is unproved and 
of what should not be made use of without proof. But the 
fact of the matter is that he who so speaks has to prove the 
impossibility of his opponent’s statements, not that they are 
not confirmed by facts, but that they are quite incompatible 
with facts or with propositions which undeniably follow from 
the presuppositions of one’s opponent, understood as he under- 
stands them—because, when possibility is denied, it is not 
enough to show the uncertainty, nor to prove the certainty. of 
other cases, impossibility must be demonstrated. In cases of 
this kind, it is one of the hardest of scientific and ethical prob- 
lems to give fair play to one’s opponent. Our own prejudices 











are sure to influence us. Yet the effect of the influence of 
another’s stand-point, when it is reached, is of immense value 
in scientific knowledge. Polemic easily leads to exasperation ; 
it is easy both to abuse it, and to let it alone, because of dislike 
to the conflicts which it produces ; but it is difficult to recog- 
nise it, and use it in the right sense as the necessary form 
which the labour of investigation always takes. Man never 
attains to a scientific knowledge of the truth without a rightly- 
conducted battle of scientifically justifiable hypotheses, the one 
against the other: the scientific guidance of this battle is the 
true dialectic method. 

For a long time the emission and the undulation hypotheses 
have been opposed to each other in optics. They are not to be 
thought of as fanciful hypotheses which present an incidental 
conception such as might coincide with the facts, without 
any warrant that ‘they actually so coincide. Both of them are 
assertions to be constructed and tested scientifically. One of 
them must contain the truth, and each of them for some time 
coincided with all observed facts, although the one appeared 
better fitted to explain one set, the other another set of 
facts. At last certain facts were found, in the phenomena 
of Interference and of Polarisation, which could easily be ac- 
counted for on the one hypothesis only, and not on the other. 
There were four hypotheses on the origin of meteoric stones. 
The one derived them from earth-volcanoes, the other from 
atmospheric vapours, the third from volcanoes in the moon, 
and the fourth gave them a cosmic origin. A stricter com- 
parison of the observed facts with what each hypothesis, de- 
veloped out into its consequences, led us to expect, showed 
that none of the first three, but only the fourth, agreed with all 
the facts of experience. They were, accordingly, seen to be 
false suppositions, while it was raised to the rank of a scientific 
theory. Inference from the effect to the only cause possible 
according to the known laws of nature is no mere hypothesis. 

In the same way the circumstance that rays which pass 
through Comets do not appear to be broken, may be explained 
either on the hypothesis that Comets are composed of a fine 


δ 134. Hypothesis. 511 





gaseous mass, Or ON the hypothesis that they are composed of 
distinct hard bodies. The latter hypothesis, although earl 
proposed, found very little support, until the identit | of 
Comets and Meteoric stones, which cause the ee of 
falling stars in the neighbourhood of the earth, favoured this 
hypothesis (although all the circumstances are not yet ex- 
plained). 
Newton did not merely show that the motions of the heaven] 
bodies, according to Kepler’s three laws, could be er 
with mathematical accuracy by the laws of RER he 
showed that a sufficient explanation could be zu only ad the 
presupposition of power which acts according to the laws of 
gravitation, and, consequently, that this sci which sufficed 
(causa sufficiens) to produce the effects, and which had been 
already shown to exist as an actual power in Nature (causa vera) 
in the power of weight upon the earth, was the only one pestihle, 
Hence the doctrine of Gravitation, which by itself could onl | 
be an hypothesis, became a scientifically established theor x 
= in this sense Newton very properly refused (in his ali 
Si, See gee eee 
| 8, 1 had been used to denote 
very many earlier fantastic assertions. The inference ra 
the perceivable consequences to the invisible cause was in this 
case absolutely certain, because this one cause only could be 
proved. The same certainty seldom enters into other depart 
ments of investigation, and it can only be reached in the is 
way. ‘ Whenever a truly great hypothesis has been esta- 
blished in any of the positive natural sciences, the science Bi 
transferred from the province of pure observations to that of 
Philosophical speculation. When the fundamental a 
of mechanics were known, and the integral calculus di di 5 
a: all that could be ascertained from the observed 
eb rei > = value τ the centripetal force for any 
we Ρ 2 successively occupied. The thought 
cae ‚when found, was to be expressed as proportional 
se wo square of the distance from the sun, and without 
o the path, so that the real path is nevertheless fully 











512 δ 134. Hypothesis. 





ascertained from this statement,—This thought is born of the 
mind.’ ! 

Herbart endeavours in his philosophy to get beyond the 
observed by means of presuppositions which are alone able to 
solve the contradictions which are contained in what is observed. 
This hypothetical enlargement of given facts, which proves 
itself to be necessary, constitutes the essence of his ‘ method 
of references.’ The apparently simple cause A, which is given, 
may not be able to establish B; but the question remains, how 
much A may be enlarged by its accompanying condition A’? 
The metaphysical application of this method, however, is very 
uncertain. | 

Every philological conjecture may be considered as an Hy- 
pothesis in so far as it finds in the text which it assumes to be 
the original one the source, not more immediately known to us, 
of those readings which are to be found in our codices. 

Every historical assertion, and assertions concerning the 
truth of reported occurrences, are Hypotheses which must be 


confirmed in this way, that they alone fully explain the actual 


shape which the report took, and the further course of the 
historical occurrence; and that they fully coincide with what 
was to be expected, as the consequence of nature, of the cir- 
‘cumstances and of earlier occurrences. That the ‘ Koresch’ 
who permitted the Jews to return from their exile and to 
rebuild the temple was King Cyrus (Kosra), although this has 
been asserted by Josephus, and is to be accepted on the 
ground of tradition, must be held to be a mere Hypothesis, so 
long as reasons worthy ef notice are brought against the 
opinion ; for the testimony of Josephus may be explained by 
the very probable psychological, though unhistorical, identifica- 
tion of a less known person with one better known, and from 
the interest Josephus had in making the well-known great 


king appear to be a friend of the Jews. The identification of 


‘Koresch’ with Kuresch, a Babylonian satrap of Artaxerxes 
Longimanus, of his suecessor Darius with Darius Nothus, the 
son of Xerxes and Esther, and, consequently, of Nebuchad- 


1 R. Lipschitz in a letter to the Author. 





δ 134. Hypothesis. 513 
nezzar with Cambyses, is an hypothesis equally justifiable 
which, if only it explains the facts, is worthy of the rank of ee 
historical truth. 

In criminal cases, the two assertions, on the one side of the 
guilt, on the other side of the innocence of the person accused 
are to be recognised as Hypotheses. The prosecutor md 
the defendant have to develope each hypothesis into its con- 
sequences, and to prove in how far their own hypothesis agrees 
with the facts obtained by observation and testimony, and how 
far their opponent’s does not. A single case of the absolute 
incompatibility of the opposite hypothesis with any one of the 
ascertained facts is sufficient to overthrow it, at least, in the 
form hitherto accepted ; but mere uncertainties and difficulties 
prove nothing. One single circumstance, which admits of one 
explanation only, is more decisive than an hundred others 
which agree in all points with one’s own hypothesis, but are 
equally well explained on an opposite hypothesis, which has 
originated from our opponent’s side of the question, 

The most essential postulate is this—We may not weaken, 
conceal, or alter any of the consequences of the hypotheses 
out of deference to the given facts, as little may we darken 
our vision for the true and simple apprehension of the facts by 
reference to the consequences of the hypotheses; nor must we 
reject every explanatory theory, nor every hypothesis pre- 
paring a way for a theory, in order to avoid collision with 
the bare facts. We must first distinctly represent, each by 
itself, both the consequences of the hypotheses and the facts 
and then carefully compare the two. It was in this way that 
Kepler proceeded when he tested his twenty different forms of 
path, which he hypothetically took to be the orbit of the 
planets. He inferred their consequences, by a most laborious 
mathematical calculation, in order to compare them with the 
observations of Tycho Brache. The difference of a few 
le determined him to test a new hypothesis in the same 
Mikes he found the true orbit: ‘sola igitur haec octo 
= er praeiverunt ad totam astronomiam reformandam.’ 

mathematical exactness in the development of an hypo- 


ΠῚ, 








514 δ 134. Hypothesis. 








thesis into its consequences is not attainable in all departments 
of research, nor is Kepler’s perseverance and his single-hearted 
search after truth a common property of mankind. The motive 
to the construction of confused notions, and to the use of am- 
biguous expressions, lies most commonly in the half-perceived 
divergence between facts and the demands of the system. 
Science, in this way, is much under the influence of the will; 
and the truth of knowledge depends upon the purity of con- 
science. The will has no power to resist scientific evidence; 
but scientific evidence is not obtained without the continuous 
loyalty of the will. 

When natural science, in the whole and in its parts, presents 
us with the lively and elevating spectacle of a genuinely sci- 
entific struggle of different stand-points, the one against the 
other, we find many cases, especially in the labours of the 
more eminent men, of a combat between opposed hypotheses 
not conducted according to logical laws. | 

Goethe, although full of the finest natural feeling, and of 
the most subtle sympathy with organic natural life, was by no 
means happy in his explanation of the genesis of physical 
natural phenomena. He very incorrectly expected to see the 
colours of the rainbow on looking through a prism at a white 
surface. He saw that the necessary condition of this phenomenon 
was the presence of a dark boundary line, and he believed 
that it gave him a proof against the Newtonian doctrine, and in 
favour of his own explanation of colours, which he said were 
the children of light and darkness; he did not rest satisfied 
with the reply that Newton’s theory also required the presence 
of a dark boundary line. The logical analysis of the case 
would have solved the apparent deception which deceived 
Goethe. According to logical laws, the Newtonian doctrine 
could only be contradicted by those facts of experience if an 
inference of the following kind could be constructed :—I! 
Newton’s hypothesis is correct the colour picture must also 
appear on looking through a prism upon an unbounded field 
of white ; this phenomenon does not occur : Therefore Newton s 


hypothesis is untenable. But the major premise of this syllo- 


§ 134. Hypothesis. 515 





gism was never, and could never have been, proved by Goethe 
for it is false. The necessity of the dark boundary line 
follows with strict mathematical accuracy from the Newtonian 
principle of explanation. The same necessity exists in both 
hypotheses, although it arises from different causes ; hence the 
fact brought forward will not serve to decide between the two : 
the ground of decision must be looked for elsewhere. 
In the struggle between scientific hypotheses, logical analysis 
very often renders essential service in settling the true value 
of single moments. A very instructive example is afforded 
by the present fluctuating discussion for and against the 
validity of the Darwinian development theory, ΒΝ ἴο 
which the higher organisms develope out of those a little ΟΝ 
by successive transformation and improvement acquired in the 
struggle for existence. This assertion! recommends itself. 
directly by its analogy with the embryonal development of 
the individual, and with the spiritual or mental develop- 
ment of civilised peoples; indirectly by the following con- 
siderations : We must either suppose that the species daten 
isms existing on this earth have existed from all eternity. or 
else that a merely periodic change is eternal, or we Er 
believe in an instantaneous procession of complicated creations 
en ee ce materials, or, lastly, 
gradual progressive development of 

the organic from the inorganic, and the higher organisms from 
the lower. The eternity of existing species? and an eternal 
periodic revolution upon the earth? are hardly reconcilable 
with geological, paleontological, and astronomical facts, for 


; Made by Charles Darwin in his work, published in 1859, Upon 
a _ of Species in the Animal and Vegetable Kingdoms by Fe 
Detection. 

* Czolbe in his work, Ueber die Grenzen und den Ursprung der 
menschlichen Erkenntniss, Jena and Leipzig, 1865, has lately dee 
tis hypothesis in a systematic construction of his mechanico-teleological 
we ei He concedes the extinction of many species and a 

ἡ small transformations of others. 

* Volger has adopted this hypothesis. 

LL2 


\ 








516 § 134. Aypothesvs. 





it presupposes the existence of this earth from all eternity, and it 
is absolutely untenable if there exists any cause which hinders 
even in the slightest degree the motion of the planets. The 
instantaneous creation of complex organisms involves an abso- 
lute miracle, transcends the circle of experience, and so is 
outside of natural investigation. There remains, consequently, 
for scientific investigation, only the last hypothesis, which is 
the Darwinian somewhat enlarged. This supposition, how- 
ever, is itself opposed by the fact, that although lesser trans- 
formations may at present be proved from experience, no great 
transformations such as it presupposes can be pointed out, and 
that while the succession of organisms in the strata of the earth 
is undoubtedly kept up, it is by no means without exceptions 
to its law. But, according to logical laws, if we are only con- 
cerned with the possibility of the hypothesis, it is an unjus- 
tifiable procedure to call these circumstances - fundamental 
objections, and to declare that their explanation is a funda- 
mental condition of the correctness of the hypothesis. For the 
previous question arises whether a properly constructed hypo- 
thesis can include the present condition of organisms which 
have become stereotyped in hard and fast lines, and which 
have been formed from organisms more fluctuating, and whose 
capacity for development only exists now within certain limits, 
and belongs more to their internal relations, and whether an 
early, and originally only sporadic, appearance of higher or- 
ganisms may not be supposed, long before the proportionate 
final destruction of many lower forms? In this last sense 
Virchow seems to vindicate the admissibility of the Darwinian 
view against the objection of Volger in his speech at the Stettin 
Association for the investigation of Nature.' 
the Darwinian doctrine has been vindicated by Héckel. 
is hypothetical, he says, only in its view of the mode of the 
genesis, and of the number of the original organisms; in other 
things it is a theory founded on facts, for it explains facts 
which can be made intelligible in no other way. Volger, on 


Tt 


il 


DO 


ı Bericht über die 38 Versammlung deutscher Naturforscher ¥ 
‚Aerzte in September 1863, p- 74 f., Stettin, 1864. 


The truth of 


| 
| 
| 
| 
| 
| 
| 
| 
| 
| 
| 


517 


δ 134. Hypothesis. 








the other hand, admits the existence of a continuous change 
of form,—species pass away and new species are formed Sica 
a common type-species: he will not allow a universal progres- 
sive development in the animal world, because hicher διῶ 
appear before the lower disappear. “It is an EEE fact 
that long before those fish-lizards existed, which have been 
looked upon as the prophetic forms out of which the pure fish 
and the pure lizards were afterwards developed, there were 
pure lizard forms belonging to the highest group of lizards 

It is a fact that the Proterosaurus is a dactylopod, and that it 
Fr, se fae Ofich onc mie te ree 
| e not to be got over. It 
is also a fact that real mammals were actually in existence 
before those mixed forms, the Ichthyosauri, which should be 
the prophetic composite typical forms of vertebrate animals 

and from which, by development combined with analysis, 
mammals especially should be produced. The Microlestes of 
x lteninger in the Wiirtemberg is as undoubted a fact as the 
Plagiaulax, related to it, and the other mammals of the Port- 


land ooli 
oolite. So long as these facts are not overthrown, a 


theory which is founded on the ignorance of these facts can- 
not be accepted.’ But Virchow’s words aim at vindicating the 
admissibility of the theory of development correctly las: 
stood, He says, ‘ We may discover by new observations that 
man existed at a time when, according to our conception 
hitherto, he did not exist. It may appear that he fought with 
the antediluvian bears, while we have hitherto μενα that 
“ie bears had vanished long before man came into EEE 
may appear the ee RE > . 
ἐπῆε Seeeamae 
; ut we must remember 
= the book of the earth lies open before us in a very few 
Bole μεν τς healt apd must be our standing-ground, 
e there alone we can find any sure knowledge of living 
velopment eens ne ba 5° οἰ mung 
universal ex u f th eee ng gers Bi 
aaa ka a = mental life ;—In the history of 
pearance in a period tae ἘΌΝ ag Eye εἰ 
g ed. They remain 


de 











518 § 134. Hypothesis. 





long unable to be understood until we see from them that the free 
development of individual men ever advances and broadens,’ 
The foundations of the theory of Hypothesis were laid by 
Plato and Aristotle. Plato denoted by ὑπόθεσις, in general, a 
supposition from which something else was deduced ; but he 
_used the word in a double sense. In the Phaedo! ὑπόθεσις 
means the presupposition of the more general, which is the 
cause of the rest, such as participation in the idea which is the 
cause of qualities. In reference to every presupposition of 
that kind a double distinction must be made. We must first 
of all consider what follows from it, and whether it agrees with 
itself or contradicts itself (—éws ἂν τὰ ἀπ᾽ ἐκείνης ὁρμηθέντα 
σκέψαιο, εἴ σοι ἀλλήλοις ξυμφωνεῖ ἢ διαφωνεῖν, and then, in 
order to confirm our hypothesis, we must lay down as its reason 
another,a higher and more general one (iris τῶν ἄνωθεν βελτίστη 
φαίνοιτο), and go on doing so in this gradually ascending way 
until we reach something in itself certain (ἱκανόν). Accord- 
ingly, Plato will not accept, and rightly, the mere agreement of 
the consequences of an hypothesis with each other as a sufficient 
criterion of the Zruth of the hypothesis ;? he does not mention 
the relation of those consequences to the facts of experience ; 
he seeks demonstration from the more universal, and by that 
first deduction only reaches a judgment concerning the admis- 
sibility of the hypothesis, which can only be proved true by its 
deduction from a higher principle. He does not, as is now 
done, prove the truth of the hypothesis by reference to the ἐν “uth 
of the consequences. The higher principle is a higher idea, 
and is at the same time a-more universal law. In the Republic 
he uses ὑπόθεσις, on the one hand, to mean what is, because it 
is the more general, the scientific foundation of the less general ; 
—fundamental notions, for example, in Arithmetic and (xeo- 
metry serve as hypotheses from which theorems may be 
deduced (ψυχὴ rein ἀναγκάζεται ἐξ ὑποθέσεων οὐκ ἐπ᾽ ἀρχὴν 
πορευομένη. ἀλλ᾽ ἐπὶ τελευτήν " -- ὑποθέμενοι τό τε περιττὸν Kal 
τὸ ἄρτιον καὶ τὰ σχήματα καὶ γωνιῶν τριττὰ εἴδη K.T.A1); and, on 


1 Pp. 100 a, 101 Ρ, 107 8. 2 Cf. Cratyl. p. 490 ©. 


3 vi. 510 sqq.; vil. 533 sqq. 


δ 134. Hypothesis. 519 





the other hand, in the opposite sense of what serves as the 
basis for the elevation of a more general—fundamental notions 
in geometry so far as they serve as spring-boards to elevate to 
the ideas. He calls this use of the words the truer, and uses, 
in the same sense of: in itself certain, equivalent to the ἱκανόν 
of Phaedo, τὸ ἀνυπόθετον, i.e. that which can no longer serve as 
a basis from which to raise to the more general, because it is 
itself absolutely the most general (τὸ δ᾽ αὖ ἕτερον τὸ ἐπ᾽ ἀρχὴν 
ἀνυπόθετον ἐξ ὑποθέσεως ἰοῦσα "---τὰς ὑποθέσεις ποιούμενος οὐκ 
ἀρχὰς, ἀλλὰ τῷ ὄντι ὑποθέσεις οἷον ἐπιβάσεις τε καὶ ὁρμάς "--- ἡ 
διαλεκτικὴ μέθοδος μόνῃ ταύτῃ πορεύεται τὰς ὑποθέσεις ἀναιροῦσα 
ἐπ᾿ αὐτὴν τὴν ἀρχήν). In this last sense the less universal 
serves as the ground of the knowledge of the more universal, 
but not as a means of testing the truth of an hypothesis from 
which it was derived—rather as a foundation, ὑπόθεσις of the 
Abstraction.' In the Dialogue Parmenides ? it is said that, in 
order to test an assertion by antinomies, not only the Assertion 
itself, but its opposite must be developed into its consequences 
(χρὴ δὲ μὴ μόνον εἰ ἔστιν ἕκαστον ὑποτιθέμενον σκοπεῖν TA συμ- 
Baivovra ἐκ τῆς ὑποθέσεως, ἀλλὰ καὶ εἰ μὴ ἔστι τὸ αὐτὸ τοῦτο 
ὑποτίθεσθαι, εἰ βούλει μᾶλλον γυμνασθῆναι) ; and, in the (non- 
Platonic) sentence quoted, this ‘ dialectic ’ procedure is defined 
to be the training or subjective preliminary conception which 
conditions scientific knowledge. 

Aristotle distinguishes (direct) demonstrative and hypotheti- 
cal inference (ἢ δεικτικῶς ἢ ἐξ ὑποθέσεως).}Σ The apodictic 
syllogism must conclude from necessary premises, and, there- 
fore, in the first place, from definitions and axioms, i.e. from 
principles true and immediately certain, which must be a 
natural prius to what is to be proved, and (as Aristotle and 
Plato both think) as such must be in itself certain:* ἀνάγκη 
μὴ μόνον προγινώσκειν τὰ πρῶτα ἢ πάντα ἢ ἔνια, ἀλλὰ καὶ 
μᾶλλον "---μᾶλλον γὰρ ἀνάγκη πιστεύειν ταῖς ἀρχαῖς ἢ πάσαις ἢ 
τισὶ τοῦ συμπεράσματοφ). The Hypothesis, however, is a pro- 

' Cf. also Meno, p. 86 E; Cratyl. p. 436 c 544. 


2 Pp. 127 sqq., 184 sqq. 3 Anal. Pri. i. 23. 
* Top. i. 1; Anal. Post. i. 2. 


= a = 
mm m I τς 











520 $ 134. Aypothesıs. 





position in which one of the two members of a contradictory op- 
posite is taken to be true, although its truth is not self-evident 
as an axiom is:! Ogcews δ᾽ ἡ μὲν ὁποτερονοῦν τῶν μορίων τῆς ἀντι- 
φάσεως λαμβάνουσα, οἷον λέγω τὸ εἶναί τι ἢ τὸ μὴ εἶναί τι, 
ὑπόθεσις. Aristotle calls that hypothetical procedure which 
was first used in Philosophy by Zeno the Eleatic, and that 
testing of doubtful propositions which have a certain appear- 
ance of truth, by their consequences, dialectical :? διαλεκτικὺς 
δὲ συλλογισμὸς ὁ ἐξ ἐνδόξων συλλογιζόμενος. 

In the same sense he calls Zeno the founder of Dialectic.‘ 
Aristotle attributes to Dialectic not only a didactic value, 
because it trains to think and is the. art of dialogue, but 
a scientific value, in so far as it is a way to the knowledge, 
and especially to the critical discovery, of principles :° 
πρὸς τρία" πρὸς γυμνασίαν, πρὸς Tas ἐντεύξεις, mpos τὰς κατὰ φι- 
λοσοφίαν ἐπιστήμας "---ἐξεταστικὴ γὰρ οὖσα πρὸς τὰς ἁπασῶν τῶν 
μεθόδων ἀρχὰς ὁδὸν ἔχει. Aristotle, however, does not solve the 
question, whether and in how far the νοῦς rocognises principles 
(ἄμεσα, ἀναπόδεικτα), or whether Induction, Dialectic, and the 
construction and testing hypotheses in the modern sense are 
required. Aristotle could not solve it; for on the one side the 
(Kantian) distinction between judgments formed analytically 
and judgments formed synthetically is an indispensable prelimi- 
nary to the solution, and so, on the other side, is the insight 
into the full meaning of deduction from what is not yet certain 
for the purpose of clearing the way for the undoubted know- 
ledge of principles—an insight due to the actual course of 
development of the positive sciences.° 

In the middle ages Hypothesis, for the same reason as In- 
duction,’ could not be apprehended in a scientific way. Ere 
logical theory could recognise the full scientific value of hypo- 
theses, positive natural science must first be preceded by the 
great fact of an earnest battle between scientific hypotheses, 


ἔστι δὲ 


1 Anal. Post. i. 2. 5 Top. i, 1. 3 Cf. Top. viii. 11, 11. 
4 Cf. above, § 11. 5 Anal. Post. i. 2. 
6 Cf. Zeller, Philos. der Gr. ii. 2; 2nd ed. p. 119. 


7 Of. § 127. 


§ 135. Proof. 521 








often prolonged for centuries, and some sure proof of the power 
of true and persistent investigation had to be given. 

Wolff‘ demanded, in opposition to the judgments of rejection 
of earlier logieians : hypothesibus philosophicis in philosophia 
locus concedendus, quatenus ad veritatem liquidam invenien- 
dam viam sternunt: but gives due warning against the misuse 
of hypothesin venditandi pro veritate demonstrata. 

Mill remarks :? ‘ Without such assumptions, science could 
never have attained its present state: they are necessary steps 
in the progress to something more certain; and nearly every- 
thing which is now theory was once hypothesis.’ 

Trendelenburg? very properly says that, ‘ whoever declares 
truth to be the present and undoubted possession of the mind 
may well fall a prey to sceptical thoughts when he becomes 
conscious of this thoroughgoing contest. But the mind has no 
inert heritage ; what it has acquired and is master of, it calls 
its own possession, This labour is its pride, and is the common 
property of the race. The form of hypothesis is the shape 
taken by every notion in the process of construction. Thus 
man grows on, regulating his conceptions by their consequences, 
and by phenomena. What he knows to be certain is revealed 
to him by this correspondence. Science advances in the same 
way when it seeks to know, not the mere conception accom- 
modated to the phenomena, but the notion of the cause. In- 
crease is made in that only which lies between the phenomenon 
and the notion of the cause, and the synthetic act of the mind 
becomes more and more complex and multiform. 

\ 


“ἢ: ' 
§ 155. Proof (demonstratio, argumentatio, probatio, 
je 


«πούειξις} is the deduction of the material truth of one 


Judgment from the material truth of other judgments. 


Direct Proof (demonstratio directa sive ostensiva, 
dr G or. > ke: eee - ᾿ 
| ὁξικτικὴ αἀποδειξις, OF ἡ ἀπόδειξις in the stricter sense, 
οἱ ἣς : 4 
PEIRTIXOL συλλογισμοι) deduces the truth of the con- 


' Log. Disc. Prael. § 127. 2 Log. 7th ed. ii. 16. 
3 Log. Unters. 2nd ed. ii. 386 f. 


ne ne en un ET - 
7 
— As = 














522 § 135. Proof. 





clusion from premises, whose truth is presupposed. It 
is genetic (demonstratio genetica) if the ground of proof 
coincides with the real cause. 

InprrEct or Aracocıc Proor (demonstratio indirecta, 
ἡ cig τὲ ἀδύνατον ἄγουσα, Or ἀπάγουσα ἀπόδειξις, ἡ εἰς τὸ 
ἀδύνατον ἀπαγωγή, ὃ διὰ τοῦ ἀδυνάτου συλλογισμός) first 
shows the material falsehood of a premise, which, the 
only one uncertain, has been combined with one or 
several undoubtedly true, from the material falsehood 
of the conclusion, and then shows the material truth of 
the contradictory opposite of that premise. By means 
of a disjunctive major premise, which includes all the 
possibilities present in the sphere under consideration, 
indirect proof, by successively excluding all the rest, 
can raise the one which remains to the rank of certainty. 


Indirect proof is quite as powerful in demonstration as. 


direct proof, i.e. it produces the same strength of con- 
viction of the truth of what is to be proved; but when 
an affirmative proposition is to be demonstrated, in- 
direct proof must be held to be inferior to the direct, 
because in indirect proof the ground of knowledge can- 
not coincide with the real cause as it can do in direct. 
Indirect proof, however, is quite a justifiable form of 
knowing the apodictic truth of negative propositions ; 
and the positive knowledge of the truth of principles 
is not to be reached without it. 

The proposition. to be proved is called the Theorem 
(theorema ). 


An inference may have formal correctness, it may be an ın- 
ference and have validity as an inference, although the judg- 
ments contained in it are materially false: but a pretended 


§ 135. Proof. 523 





proof, whose elements have no material truth, is not a valid 
proof. The so-called argumentatio ad hominem (κατ᾽ ἄνθρωπον), 
in opposition to the argumentatio ad rei veritatem (κατ᾽ ἀλή- 
θειανῚ, is not a logical form. 

The method of Euclid in Mathematics is the most perfect speci- 
men of accuracy in denionstration. In this reference the work of 
the Alexandrine geometer is unsurpassable. An impartial es- 
timation however will scarcely confirm the judgment of Käst- 
ner unconditionally :' ‘Every text-book of Geometry possesses 
less of what is of the most value in Geometry, distinctness and 
certainty, the further it departs from the Elements of Euclid.’ 
It will rather corroborate the judgment of the Cartesians,? that 
itis a mistake on Euclid’s part: ‘ Avoir plus de soin de la 
certitude que de l’Evidence, et de convaincre l’esprit que de 
’éclairer ;’ that he has given too little: ‘ Des raisons prises de 
la nature de la chose méme pourquoi cela est vrai ;’ and “ N’avoir 
aucun soin du vrai ordre de la nature.’ Euclid has sacrificed, 


in order to obtain this one requisite of strict accuracy (of course 


the most essential), others which are not incompatible with it. 
T'schirnhausen desiderates, next to the greatest possible gene- 
ralisation, the deduction of every proposition from that doctrine 
on which it most naturally depends (cf. Chasles, Geschichte der 
Geometrie, p. 112, Halle, 1839); and Schopenhauer, in the very 
same sense, requires geometry to base its propositions on existence 
and not to enunciate ‘ mousetrap-proofs ’ ( Mausefallenbeweise). 
Proofs should not only be strict, but, where possible, should 
be genetic, ie. the ground of knowledge should coincide with 
the real cause. This postulate should and must raise the 
modern science to a higher rank than Euclid was able to do. 
A more genetic demonstration is rendered possible by means of 
analytic geometry and the calculus of infinitesimals. For 
analytic geometry separates the essential and universal relations 
of quantity which may be represented in formulae, from the 
accidental forms which they take in single figures. It leads 


ἢ Anfangsgr. der Geom. 4th ed. Ρ. 428; cf. Trendelenburg’s Log. 
Unters. 2nd ed. ii. 365; 8rd ed. ii. 399. | 
* Log. ou U’ Art de Penser, iv. 9. 


. un a 
---. 


a a nr 
en τονε, 


AF A ent em en A Meran. . 
Nee eee eee 


ΕΟ 
ae m 


em 
ὡ»- .- 


ORM ων. ον. 





ΟΝ 





ee ne 


eran Ha see Ὁ 
a = == = τὰ 


een = 


§ 135. Proof. 


us, over and beyond the manifold and various considerations, 
‘accidental views,’ and auxiliary inventions happily discovered 
in individual cases, on which most constructive proofs are 
based, to the surer and more uniform knowledge of particulars 
from their common general causes; while the differential and 
integral calculus leads us back to the last elements in order to 
understand the genesis of mathematical notions, and so to com- 
prehend their essence and relations, and thereby to prove the 
theorems which rest upon them. It is here, therefore, that we 
can see the greatest simplicity of proof accompanied by the 
most complete satisfaction to the thinking mind. 

Every indirect proof is obtained by means of an Hypothesis.' 
This hypothesis is not enunciated in the hope that it will per- 
haps be confirmed by the truth of its logical consequences, but 
with the express view of overthrowing it by proving the false- 
hood of one of its consequences, and in this way finding the 
true assumption by the exclusion of the untenable ones. This 
procedure serves to establish principles in a scientific way, 
because they, since they are highest and most universal, do not 
admit of deduction from any higher proposition, and because 
mere Induction, taken by itself, is not sufficient. The true 
nature, for example, of infinitely small quantities, or of the 
differential as a flowing quantity, is shown by means of the fol- 
lowing indirect proof. The differential is either of a fixed or 
of a flowing value. If it is a fixed quantity, it must either be 
equal to nothing, or in its absolute value greater than nothing. 
It cannot be nothing, because it has definite relations to other 
differentials, whereas the relation of nothing to nothing is quite 
indefinite. (For example, 2*dx can never be made =dx, 
whereas 2°0=0. In the same way, the infinitely small circle 
has its definite relation to its semicircle, the circumference its 
relation to the radius and its separation from it and from the 
centre, &c., whereas in the mere point whose extent is =0, all 
these relations vanish.) But the differential cannot be a fixed 
quantity different from nothing, because it would not then 


O 
absolutely disappear in the presence of a finite quantity, and 


1 Of, § 134. 


‘§ 135. Proof. 525 








because in many cases the asvertained result would not be 
absolutely accurate, whereas its absolute accuracy is from 
another side apodictically certain (e.g. by means of a proof 
given in a purely elementary way without the aid of the dif- 
ferential calculus). Hence the differential is not a fixed quan- 
tity, but is to be thought of as a flowing one; i.e. that quantity 
is infinitely little which is determined by going through a 
series the limit of the value of whose members is zero—that is, 
a series which has the two following properties:—1. That a 
member furnished with the same index, and of smaller absolute 
value, follows every member of the series; and, 2. That what- 
ever fixed number be given, however small this number may 
be, a member of the series is always to be found whose absolute 
value is still smaller. 

A teleological argument for the existence of God may be 
given indirectly. In the Kantian disjunction: the world is due 
either to accident, or to a blind necessity, or to a free cause 
it may be laid down and proved that neither the first nor the 
second assumption corresponds to the given characteristics of the 
universe, while the third does. The harmonious construction 
of organisms is only intelligible from the thought “by which 
all problems in physics are at bottom solved,’ and the finite 
spirit is only comprehensible from the eternal spirit of God. 
Still Logic, in so far as it is a doctrine of knowledge, notices 
this problem only as an example in method. It is not an 
integral part of its task.! 

Aristotle explains Demonstration (amoösıEıs) to be a species 
of the syllogistic procedure, and finds its specific difference in 
the material truth and necessity of its premises :? ἀπόδειξις μὲν 
οὖν ἐστιν, ὅταν ἐξ ἀληθῶν καὶ πρώτων ὁ συλλογισμὸς 7, ἢ ἐκ 
τοιούτων, ἃ διά τινων πρώτων καὶ ἀληθῶν τῆς περὶ αὐτὰ ke 
τὴν ἀρχὴν εἴληφεν" διαλεκτικὸς δὲ συλλογισμὸς ὁ ἐξ ἐνδόξων 
ὸ υλλογιξόμενος.3 ἀνάγκη τὴν ἀποδεικτικὴν ἐπιστήμην ἐξ ἀληθῶν 
7 εἰναι καὶ πρώτων καὶ ἀμέσων καὶ γνωριμωτέ ὶ ; 

ριμ P@V Kal TT POTEP@V 

' Upon the problem itself and the method of its solution, cf. Trende- 


le) rer r >. : 
Ἢ μὰ Log. Unters. 2nd ed. ii. 406 f., 425 ff; 8rd ed. ii. 441 f, 461 ff. 
0}. 1.1. 3 Anal. Post. i. 2. 

















526 ὃ 136. Refutation, Investigation, Problem. 





καὶ αἰτίων τοῦ συμπεράσματος. Aristotle distinguishes direct 
and apagogie demonstration :! ἀνάγκη δὴ πᾶσαν ἀπόδειξιν καὶ 
πάντα συλλογισμὸν---δεικνύναι---ἢ δεικτικῶς ἢ ἐξ ὑποθέσεως" τοῦ 
᾿ ἐξ ὑποθέσεως μέρος τὸ διὰ τοῦ ἀδυνάτου..----πάντες γὰρ οἱ διὰ 
τοῦ ἀδυνάτου περαίνοντες τὸ μὲν ψεῦδος συλλογίζονται, τὸ δ᾽ ἐξ 
ἀρχῆς ἐξ ὑποθέσεως δεικνύουσιν, ὅταν ἀδύνατόν τι συμβαίνει τῆς 
ἀντιφάσεως τεθείσης. He prefers direct to apagogic demonstra- 
tion, in so far as direct demonstration infers from what is better 
known and earlier, or from what is more allied to principles 
(ἐκ γνωριμωτέρων καὶ προτέρων)" The highest principles of 
demonstration are in themselves indemonstrable, and as imme- 
diately certain propositions (ἄμεσα) are known by the voos, 
they must be better known in themselves, and more self-evident, 
than what is deduced from them.? 

Wolff,‘ in order to make the definition of Demonstration 
conformable with the terminology of the positive sciences, re- 
quires from it only the truth of all its premises, and admits, 
besides definitions,? axioms, and theorems deduced from them, 
premises which are based on undoubted facts of experience. __ 

Kant® explains the dangers of indirect demonstration, and, 
going too far, would exclude it from pure philosophy. 

Trendelenburg’ has given special attention to the meaning and 
value of indirect demonstration in the knowledge of principles. 


$ 136. REFUTATION (refutatio, ἔλεγχος, ἀνασκευή) 18 
the proof of the incorrectness of an assertion or of a 
demonstration. 

The refutation of an assertion is identical with the 
(direct or indirect) proof of its contradictory opposite. 

The refutation of a demonstration is accomplished 
either by weakening the deduction, i.e. by showing that 

1 Anal. Pri. i. 23. 2 Anal. Post. i. 23. 

3 Ibid. i. 2 sq.; of. $ 134. 4 Log. § 498. 

5 He follows the example of Melanchthon, Erotem. Dial. I. iv. 23). 


6 Krit. der rein. Vern. p. 817 ff. 
7 Log. Unters. 2nd ed. 11. 396 ff, 425 ff. 


§ 136. Refutateon, Investigation, Problem. 





what was to be proved does not necessarily follow from 
the premises, or by proving the material falsehood of 
some premises. 

INVESTIGATION (disceptatio) and scientific disputation 
consist in weighing the causes for and against an 
assertion. 

In any thoroughgoing contradiction of an opposed 
assertion, the refutation of the demonstration must 
be united with the demonstration of the contradictory 
opposite. Refutation is most complete when it shows 
the cause of the error, and so destroys the deceptive 
appearance of correctnéss. 

The knowledge to be produced by a scientific inves- 
tigation is called the PROBLEM. 


The true apprehension of the opposite opinion, the capacity 
to get thoroughly within, and in a measure to sympathise with, 
the circle of another’s thoughts, is an indispensable condition 
to genuine scientific polemic, but one seldom fulfilled. The 
power of fulfilling this requisite arises only from a disinterested 
love of truth. Nothing is commoner in difficult problems than 
a half and one-sided apprehension of thoughts strange to 
us, confounding it with a part of our own opinion, and then 
combating this chimera. The opinion disputed is classed 
under some abstract category or other, which looks suspicious 
to common judgment or prejudice; or else an introduction 
branding it as heretical is prefixed to a garbled statement, 
in order to prevent the impression which the thought itself 
even in this form might make, and to confuse the pure sen- 
sibility. The contest is transferred to a different province, 
and, by its construction of suspected consequences, polemic, 
which ought to serve for the common investigation of truth, 
15 degraded to be an instrument for making attacks on indivi- 
duals, The experience of all times shows that these perversi- 
"es are not solely produced by a specially dull and narrow 





m ee rn an 


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an A IE 
m τπππττοΣι 


a mn 





528 § 136. Refutation, Investigation, Problem. 








power of thought, and a specially weak and degenerate will. 
It is a rare power and structure of thought and conscience 
which can keep itself entirely free from them. It is natural 
to believe that he himself, or the community to which he 
belongs, is fully in the right, and that, consequently, his 
opponents are to be looked on as enemies of the truth, to 
enquire any more deeply into whose absurd opinions is at 
least an unnecessary trouble, and is perhaps a violation of 
truth and loyalty to one’s own community. In more favour- 
able cases they may be looked onas we would on sick persons, 
or on the feeble-minded, or their opinions may be considered 
to be behind the age, and occupying ἃ stand-point which 
we have got wholly beyond, towards whom, provided that 
they are not stiff-necked on their side, a certain degree of 
humanity, in the shape of a good-hearted forbearance and con- 
sideration, is to be shown. To overcome narrowness, and to 
enter fully within the circle of an opponent’s thoughts, and 
into the motives for his doctrine—which is a very different 
thing from the languid toleration of indifferentism—presup- 
poses a height of intellectual and ethical character, which is not 
innate either in individuals or in the race of man, but must 
be acquired by a long and earnest struggle in development. 
Yet this is the only path which leads man to truth. ag 
judgment only emancipates who has shown himself to be docile. 

When the Problem rests on the opposition of cause and 
contradictory cause, it hears the character of an antithesis. 
The necessity of solving the contradiction is the greatest spur 
to scientific research. An example of an unsolved antithesis 
lies in the relation of the cosmogony to the want of any experi- 
ence of an original creation. . 

A theory, to be thoroughly tested, must be tested in a two- 
fold way. On the one hand, the arguments must be tested,— 
Are they able to prove what they are adduced to prove? On 
the other hand, the doctrine itself, the substance of the propo- 
sition constructed upon those arguments, must be tested,—ls 


! Karl Lachmann in the preface to the 2nd ed. of the Jwein; cl. 
Hertz, Biogr. p. 179. 


§ 136. Refutation, Investigation, Problem, 529 








it free from all internal contradiction, and is it free from 
any incompatibility with facts? It is clear that what has 
been really accurately proved must be free from contradiction, 
and that what involves a contradiction cannot be accurately 
proved. Hence a positive result from the first process of 
testing would render the second superfluous, while a negative 
result from the second process would render the first super- 
fluous. But we should remember our liability to error, and 
should so complete our process of testing in both ways, that 
what remains undeterminate by the result of the one may be 
determined by the other. 

Aristotle defined refutation,! ὁ γὰρ ἔλεγχος ἀντιφάσεως συλλο- 
γισμός---ἔλεγχος δὲ συλλογισμὸς μετ᾽ ἀντιφάσεως τοῦ συμπερά- 
ouaros” He demands that Logic should point out the way 
in which others have fallen into error,’ ἀλλὰ καὶ διότι ψεῦδος 
ἀποδεικτέον, and:* οὐ μόνον δεῖ τἀληθὲς λέγειν, ἀλλὰ καὶ τὸ 
αἴτιον τοῦ ψεύδους κ.τ.λ. Among others Wolff, who calls this 
procedure ‘ praestantissimum refutandi modum,’ follows his 
example. Wolff, however, prefers a demonstration of the 
truth to every kind of mere refutation, and does so Justly.® 

Kant? urges that, in order to destroy errors, apparent truth, 
the source of error, should be investigated and explained, and 
has sought to accomplish this® demand by means of his so- 
called ‘dialectic inferences of reason.” He proposes to him- 
self, by means of a thorough-going investigation, to trace the 
true causes of the delusive errors which arise “in the fallacies, 
not of men, but of the pure reason itself.” In this way delusive 
error, although (like optical deception) it cannot be removed, 
will no longer lead us astray. The carefulness and thorough- 
ness of this investigation of Kant’s, so far as its formal nature 
Sees, commands the admiration and respect of those who must 


reluse to agree with the material contents of the Kantian 
doctrine, 


I Anal. Pri. ii. 20, 

3 Top. Vili. 10, 160 B, 37. 
5 Logica. § 1088. 

" Log. Einl. vii. Β. 


2 De Soph. ΕἸ. ce. i. 

4 Eth. Nie. vii. 15. 

6 Ibid. § 1035. 

° Krit. der rein. Vern., transse. Dial, 
MM 


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530 ὃ 137. The most notable Errors in Proof. 





$ 137. The FALLACIES which one may fall into lie 
either in the mode of deducing the conclusion from the 
premises, or in the premises, or in the conclusion. 

Fallacies of the first kind comprehend the Paralogisms 
and Sophisms explained above ($ 126), and fallacies of 
induction in inductive proof ($ 130). 

Fallacies of the second kind have to do either with 
material truth of the premises themselves or the cor- 
rectness of their assumption in the case under con- 
sideration. 

A pretended proof from false premises is called fal- 
lacia falsi medit, when the invalidity consists in com- 
bining the middle term with the other notions. In 
indirect proof one of the most common and most pre- 
judicial fallacies arising from incorrectness in the 
premises results when an incomplete disjunction in the 
major premise is erroneously supposed to be complete. 
An incorrect premise, on which a series of various 
consequences is based, is called a fundamental error 
(error principalis, or fundamentalis, πρῶτον ψεῦδος. 

A proposition which may be materially true cannot 
be assumed to be true, and cannot be used as a premise, 
when it is either identical, in point of fact, with the 
proposition to be proved, or when its truth may be 
questioned along with the truth of the proposition 
to be proved. This is the logical postulate—assume 
nothing which is to be proved. Its neglect is the fallacy 
of assuming the point in debate (τὸ ἐξ ἀρχῆς sive τὸ ἐν 
ἀρχῇ [scil. προκείμενον] αἰτεῖσθαι, petere id quod er 
strandum in principio propositum est, petitio principil, 
argumentari ex non concessis tamquam concessis). 


δ 137. Zhe most notable Errors in Proof. 531 





Reasoning in a circle (circulus sive orbis in demon- 
strando) is related to the last fallacy. It proves a by 
3, then B again by A, or A by B, B by c, c a patel 
and D or any other element in the demonstration by A. 

Fallacies of the third kind consist in making a diver- 
sence from what is deduced from the premises to what 
is to be proved, and in the substitution of the latter for 
the former (heterozetesis, ἑτεροζήτησις). 

The divergence is either qualitative (μετάβασις εἰς 
ἄλλο γένος) or guantitative—proving too much or proving 
too little. When it occurs in a regular refutation, then 
it may be either the (unconscious) zgnorance or the 
(conscious) change of the point in debate (ignoratio sive 
mutatio elenchi, 7 τοῦ ἐλέγχου ἄγνοια μεταβολή). The 
confusion of the refutation of a pretended demonstration 
with the refutation of the fact to be demonstrated is an 
instance. When too little is proved the purpose of the 
demonstration has not been sufficient; but what is 
actually proved is not to be absolutely rejected. It has 
its own value, and may, perhaps, serve as a stepping- 
stone to a fuller knowledge. When too much is proved, 
if the whole result is correct, no harm is done. What 

is to be proved is usually able to be obtained by Sub- 
alternation or Partition from the more comprehensive 
result. But when the result contains materially false 
elements, it will show the characteristics of some one 
or other of the various formal or material fallacies in 
demonstration. In this sense the proposition is true; 
‘Qui nimium probat, nihil probat.’ 
Subreption (subreptio) is a common name for con- 


cealed fallacies of. any kind, in so far as a sight of the 
MM2 

















532 § 137. Lhe most notable Errors in Proof. 





desired result has led the reasoner astray; but it is more 
particularly used of different forms of Heterozetesis. 


Truth as well as falsehood may result from false premises,' 
For example, from the systems of the Universe, conceived by 
Ptolemy and Tycho de Brahe, the nature and periods of eclipses 
of the moon, the duration of the month and of the year, could 
be deduced with a certain degree of accuracy. In cases of 
this kind the falsehood of the arguments co-exists along with 
the truth of the proposition which is not really proved by them. 

Indirect proof, when it seeks to establish a positive ng 
by the exclusion of all other conceivable cases, age A 
strict disjunction of the different possible cases. It is 0 a 
the hardest part of the task to fulfil this condition with the 
strictness required. Indirect proofs are not dangerous in ee 
thematics where a complete representation of the possible as 
may generally be given without difficulty, and si ig 
certainty; but they are misleading in other es - : 
sciences, and especially in sciences such as Philosophy pr 
Theology, where, after a slight modification of n en. 
arguments directed against it, perhaps ee er = 
previous form, are no longer appropriate, and the in sen? | 
the truth of the opposite opinion has no logical va u 
The witness borne by the oldest opponents οἵ emg ᾿ 
his guilt rests on an incomplete disjunction. mpgs : ney 
believed must either have the sentiments of the ok an ἐς 
Athens or be ἃ sophist. Now, he had not the first: sai 
fore he must be the second. The delusion was gin y 
necessary because here, as in all similar cases, “er =. 
stand-point which rises above and combines the a ΡΝ : 
one-sided views cannot be understood by those ae . ; : 
any of the opposed opinions, since he who = Loge = 
already raised above them. The apparent ir in nat 
cessity of the χωρισμός of the Idea (cf. above at § 5 ) 2 
on the incomplete disjunetion: Ideas existing by t ve i a 
(universalia ante rem)—individuals of sense, overlooking 


I Cf. above, N 138. 


§ 137. The most notable Errors in P 7007. 533 








ideas inherent in real existence (universalia in re). The ap- 
parent proof for the necessity of despotic forms of communities 
depends on the incomplete disjunction: divine order—human 
caprice, where the third possibility of rational volition is 
neglected. A very instructive example is afforded by the 
lunacy physician, Maximilian Jacobi, whose decision was very 
famous in its day. When examining the mental condition of 
a criminal, Reiner Stockhausen, who had been brought to his 
establishment, he declared that he was not insane, but quite 
able to account for his own actions because his case did not 
correspond to any of the six forms into which he himself had 
classified mental diseases. (He thus overlooked mixed forms. ) 
When brought to the House of Correction the patient soon 
gave evidence of his insanity.! 

Kant warns men against apagogic demonstrations in philo- 
sophy, but the proofs which he himself adduces for the funda- 
mental propositions of his system are apagogical, and suffer 
from the fallacy of incomplete disjunction in the major premises 
which are stated. Logic, according to Kant, has nothing to 
do with the objects of knowledge. Therefore it has to do only 
with the understanding in itself and in its forms. But a third 
possibility has been overlooked, that while the objects them- 
selves do not make the object of Logic (and while the task of 
Logic is not identical with that of Metaphysics, Mathematics, 
Physies, History, &c. ), it is not thinking purely in its relation 
to itself or its freedom from contradiction, but rather the 
relation of thinking to existence, the agreement of thought with 
its objects, that is to be explained in Logic. According to Kant 
experience is not, and therefore forms of thought, which belong 
ἴθ us ἃ priori or independently of all experience, are the basis 
of the apodicticity of our knowledge. Here also a third possi- 
bility is overlooked: the ground of apodictic certainty may lie 
in the order of things—in themselves and the regular manner 
of sense-affection ; we may recognise this order by a thinking 


I C£. the tract, Ueber Reiner Stockhausen, Elberfeld, 1855, for the 
one side, p. 119 ff, and for the other, p. 133 ff., where Dr. Richarz 
points out the dangers attending the method of exclusion. 





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Se 7 ee 0 eer Bee a gr του ταν 
= ar: == — Fe aa © τι Θ᾿ ΞΡ ρτ  τπατ τ: 


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er 


534 8137. The most notable Errors in Proof. 





based on experience, whose action, which is subject to the sum 
total of the logical rules (regulative laws), systematically 
linking experience together according to relations lying in 
experience itself and found there, does not need to be hypos- 
tatised into a series of ‘a priori forms,’ which must be added 
to the given material as a second ‘ constitutive element.’ Just 
as in the mechanical arts what cannot be done by mere hand 
labour is accomplished by the hands and machines, which were 
themselves originally produced by the hands, and not without 
the hands by magic, so we do not attain to that measure of cer- 
tainty, which the merely single experience could not give, by 
means of an a priori magic independent of all experience. We 
obtain it by thinking, which combines experiences according to 
logical laws. According to Kant, in the Kritik der praktischen 
Vernunft, a material ground of determining the will, i.e. one 
directed to a desired end, is not capable of being the principle 
of morality, and therefore the only possible principle of morality 
is the form of strict universality of law possible without con- 
tradiction. Here also the disjunction is complete. A third 
possibility remains unnoticed, that the principle of ethics is to 
be sought neither in a mere formless material, nor yet ina 
form void of all content, but in the relations which subsist 
between various aims, or in the gradual series of their value.' 
An example of a πρῶτον yebdos, from which a series of 
other errors is derived with a relative necessity, lies in the 
naive assumption which is formed from the deception of the 
senses, and confirmed by the natural vanity of men, that the 
earth stands still, and is the central body in the centre of the 
universe, and that the heavens revolve round it in a circle. 
The Cartesians made use of a PETITIO PRINCIPII in their 
polemic against the Newtonian doctrine of gravitation when 
they looked at the proposition: a body at rest: can neither 
move itself nor any other, as a necessity of thought, founded on 
the axiom that nothing cannot be a cause of anything, and on 


1 Cf. App. D, and the author’s article, Das Aristotelische, Kantische 
und Herbartische Moral-Princip, in Fichte’s Zeitschrift, xxiv. 71 ἢ. 
1854. 


§ 137. Lhe most notable Errors in Proof. 535 





the notion of matter, which was fully and exhaustively given in 
the definition: ‘extended substance’—while the chief ques- 
tion in debate was not the validity of this notion of a matter 
only extended, or of a matter absolutely without power. Kant’s 
attempt to prove his opinion that the First Figure of the Cate- 
gorical Syllogism is the only regular one! is another example 
of the Petitio Principii. He founds his opinion on the asser- 
tion that the law of the First Figure, which enjoins that the 
Major Premise must be universal and the Minor affirmative 

must be the law of all categorical inferences of the seins 
But this assertion arises from the definition of the inference of 
the reason as ‘ the knowledge of the necessity of a proposition 
by subsuming what conditions it under a general rule ’—a de- 
finition which of course applies to the First Figure only and 
to none of the others. It contains, however, an arbitrary 
limitation which assumes the very thing Kant has to prove; 
viz, that there are no simple and regular syllogisms in the 
other Figures, and that the division of Figures saab four is a 
‘false subtlety.’ A Petitio Principii is contained in the objec- 
tion to the teleological argument :? ‘since the absolute conforma- 
bility to plan in nature is only the necessity of things, no 
inference can be made from the conformability to plan of the 
world to a supernatural cause.’ For the ‘ only’ may be called 
in question. Anton Rée says: ‘ When an article cannot be 
tabricated for as little as it costs to bring it from abroad, 
inclusive of the carriage, it is decidedly better to procure it in 
the latter way, and rather produce what our land is better able 
to yield and what we may be able to export.’ But the real 
question is, does such a thing exist? and does it exist in such 

proportion that the equilibrium between production and con- 

or 15 to be produced neither by excessive emigration nor 

ese unget-typhus ? site implicitly assumes as granted, 

y a very heedless opponent will grant, and what ought 


5 
Von der falschen Spitzfindigkeit, §c., and Logik, § 56 ff. 

a Kirchengesch. des neunzehnten Jahrh., Ρ. 357, Tiib. 1862. 
__'Fanderungen auf dem Gebiete der Ethik, ii. 147 ἢ, Hamburg, 


1857 " 





536 § 137. The most notable Errors in Proof. 





to be the chief question to be proved. He commits a Petitio 
Principii. 

A REASONING IN A CIRCLE happens when we assume, 
with Des Cartes, the (objective) reality of what we know with 
(subjective) clearness and distinctness, or of what is a (subjec- 
tive) necessity of our thought; when we found the proof for 
the existence of God, or for the validity of the idea of the 
Absolute, on this supposition; and when this supposition is 
then established by reference to the truthfulness of God, or 
by the notion of making absolute harmonious the opposition of 
subjectivity and objectivity. 

Zeller finds a μετάβασις eis ἄλλο γένος! when Ast in- 
sists on taking the Socratic δαιμόνιον substantially in Plato, 
after the analogy of passages in Xenophon; for the inference 
of analogy only warrants us in giving the same meaning to 
different passages when they occur in the same author. When 
the hermeneutical principle of the ‘analogy of the faith’ is 
extended too widely, it becomes the same fallacy. 

An IGNORATIO OR MUTATIO ELENCHI occurs when a proof 
refuting the hypothesis of innate ideas is opposed by saying 
that the ideas have their value, and that the true value of our 
thought and action depends upon their theoretical and practical 
recognition. It occurs when we oppose the assertion that there 
is no synthetic knowledge ἃ priori, or that there is no transcen- 
dental freedom in the Kantian sense, by proving or asserting 
that science cannot exist without apodictic certainty, nor mo- 
rality without the determination of the will by ideal motives. 
It occurs when it is said that to deny the existence of know- 
ledge & priori (in the Kantian sense) leads to the absurdity of 
wishing to prove by the reason (a priori) that there is no reason 
(no knowledge a priori). For the question in debate is not the 
validity of the ideas, nor the existence of an apodictic certainty, 
nor of the faculty of reason, nor of the ethical freedom of the 
will. We confuse our opponent’s opinion with part of our own 
when we substitute our own prejudice that the validity of the 
ideas depends upon their special origin, or apodicticity upon 


! Philos. der Griechen, 1st ed. ii. 29. 


§137. Lhe most notable Errors in Proof. 5 37 





ä priority, and morality upon the unnecessitated removal of the 
causal nexus, for the whole of our opponent’s opinion ; and having 
made this confusion, we now argue as if the refusal to admit 
the false explanation necessarily pointed to the denial of the 
facts themselves (which, however, have been indeed denied by 
some of those who objected to the above-mentioned explana- 
tions). Theopomp, the disciple of Isocrates, endeavoured to 
show that the Platonic explanation of ethical notions was use- 
less, by the argument, that these notions were universally able 
to be understood without definitions. But Epictetus, the 
Stoic,' objected to this objection, as an ignoratio elenchi, when 
he insisted (in accordance with the Platonic distinction between 
science and correct opinion) on the distinction between ἔννοιαι 
φυσικαὶ καὶ προλήψεις, which we have without philosophy, and 
the definite conscious knowledge of essences, at which philo- 
sophy aims. Another example of mutatio elenchi occurs in the 
substitution for the refutation of untenable arguments the 
refutation of the opinion itself, supported by those arguments. 
For example, a demonstration of the invalidity of supposititious 
proofs for the existence of a generatio aequivoca sive spontanea 
(the development of organic forms from dissimilar organic or 
from inorganic material) is often substituted for the proof of 
the non-existence of any generatio aequivoca sive spontanea. 
The physico-theological argument proves TOO LITTLE. Tt 
does not mention the ethical attributes of God. But in so far 
as it actually shows the certainty of a divine might and know- 
ledge, it is not to be wholly rejected (as Kant does) for the 
sake of the moral argument, but is rather to be complemented 
by it. Another species of the fallacy of proving too little 
occurs in Zeno’s pretended demonstration that Achilles can 
never overtake the tortoise, for whenever Achilles has reached 
the place where the tortoise has been, it has made another 
advance. A mere appeal to the parallelism in the infinite 
divisibility of space and time does not suffice to solve this very 
deceptive fallacy ; for Zeno could object that, in accordance 
with this uniformity, the swifter object may reach the slower 


I Enchir. ii. 17. 


-“οαδνα,.......2........»......... 


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538 § 137. Zhe most notable Errors in Proof. 





neither at any time nor at any place. But, in fact, Zeno’s 
argument only proves that, if the two velocities are to each 
other as 1:n, the one will not overtake the other within the 
following series of divisions of time and parts of the way :— 
1 1 
+— + 


n i n? n? 





+ ....ıininfin., 


where ine original distance is conceived as a unit of length or 
as measure of the way, and the time in which the swifter object 
traverses this unit of length as the unit of time. By omitting 
the clause: within this series, the universal proposition is sub- 
stituted that the one can never and nowhere overtake the other. 
The omission would only be correct if it were proved that the 
sum of that series is infinite, i.e. that, whatever fixed quan- 
tity be given, the series developed indefinitely must have a 
sum which exceeds that quantity. Zeno has not proved this, 
nor can it be proved; for what is to be proved is false, and its 
opposite may be shown to be true with mathematical accuracy. 
The sum of that series, infinitely extended, does not exceed a 


definite number, viz. — Τ᾽ and only approximates to any fixed 


n— 
difference. Hence it only follows that before a certain finite 
series of times determined by that quantity has elapsed, and 
before a corresponding path has been traversed, the quicker 
object does not attain the greater distance. This is thoroughly 
true, but is too little when compared with what Zeno wished to 
prove, and believed that he had proved. But the deception 
arises in this way. Is that quantity of time and that quantity 
of space, which, so long as we keep within that series, is un- 
attainable, absolutely unattainable ?—or must we always keep 
within the series? Then this is connected with an innumerable 
number of members, and with the necessity, when these are all 
individually represented, to attach to every advance, however 
speedy, a finite and approximately equivalent short time, and 
also, when the infinite number of divisions of space are in- 
dividually represented in actual separation, of representing every 
one by a finite and, as nearly as possible, proximately equiva- 


§ 137. Zhe most notable Errors in Proof. 539 





lent section as small as possible. he series resulting in this 
way is absolutely unable to be gone over, because its sum (not 
merely its number of parts) is an infinite quantity. What is 
true of this latter series is unconsciously transferred, by those 
who fall into this fallacy, to the first. 

Feuerbach’s argument against the reality of the idea of God, 
because it is only an hypostatising of our own existence, is a 
youcher on bebalf of the logical proposition: ‘qui nimium 
probat, nihil probat.’ In the logical form used, this argument 
forms the major premise, which, as such, should be universally 
true: The multiplication of our own essence in a gradual scale, 
according to the measure of phenomena, is not a valid form of 
knowledge, it is only a poetical fiction. But this major premise 
is untenable, because many other assertions which are evidently 
false would follow from it (cf. above, ὃ 42). Hence the argu- 
ment is not convincing, and the decision of the question must 
be sought on other grounds. 

Bonitz! refutes an argument of Spengel’s by the proof that 
it would prove too much, and therefore that the universal pro- 
position, on which it tacitly rests, is false when he says: ‘ He 
who requires the expression ἐξωτερικοὶ λόγοι (in Aristotle) to 
have the same meaning in every connection, must also give the 
same meaning to τὰ φυσικά, ἀνατομαί, etc., in every connec- 
tion—a demand which can evidently not be complied with.’ 

SUBREPTIONS of all kinds are unavoidable when whole 
systems are deduced from one or a few principles only, while 
the particular cases which are subsumed under that universal 
are not reached in any other way (either hypothetically or 
empirically), The problem of the ‘ dialectic method,’ at least 
when understood in this sense, is insoluble (cf. above, § 31). 


1 In the Zeitschrift 7. dst. Gymn. p. 227, 1866. 


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δ 138. Definition of System. 





PART SIXTH. 


SYSTEM IN ITS RELATION TO THE ORDER OF THE 
OBJECTIVE TOTALITY OF THINGS. 


§ 138. System is the orderly combination of mutually 
related knowledge into one relatively complete whole. 
Science is a whole of knowledge in the form of the 
‘system. System is meant to represent in its articula- 
tion the articulation of the totality of its (natural or 
mental) objects, according to the ‘ Law of Totality.’ 
Scientific knowledge finds its perfection in the com- 
bination of thoughts, one with the other, into a whole, 


which in its content and form represents the objective 


reality. 


Scientific propositions and System are related to each other as 
content and form. But the right form is essential to the content. 
It is not merely the sum of individual cognitions of scientific 
significance, nor is their systematic concatenation of merely 
didactic value. Science, as such, has its true existence only in 
the systematic form. If (as Nominalisın assumes ) individuals 
only have real existence, and the sum total of reality is.a mere 
conglomerate of singulars, or if (as the Critical Philosophy 
asserts) all and every arrangement, down to the form of. the 
individual existence itself, is to be looked at as a merely sub- 
jective accident imposed by ourselves, then System would have 
a subjective significance only. But the forms of existence 
really belong to the reality to be known, and it exists in them. 


The Law of Thought of the Totality. 





For the same reason Thought is not (as the Sensualist Philo- 
sophers say) merely a reflex of perception ; it is this mere reflex 
where perception is the adequate form of knowledge (e.g. in 
testimony to a deed done the testimony is only.a substitute for 
eye-sight) ; but it is not so in the apprehension of such forms as 
have corresponding forms of thought (e.g. in a concatenation of 
mathematical figures which is to become known by demonstra- 
tion, where the figure only serves to give sensible appearance, or 
in the knowledge of a causal-nexus, where the perception of suc- 
cession is itself only a reflex of the thought). In the same way 
thought is not (as a one-sided Intellectual Philosophy assumes) 
without an empirical basis sufficient for any scientific knowledge 
whatsoever. The several forms of knowledge are necessarily re- 
lated to the individual forms of existence, and so is system to the 
sum total of them all, or to the orderly concatenation of things. 
Whoever does not know the real articulation of the objects of 
any science, has not only lost a very useful aid in enabling 
him to learn it, but has not acquired an essential element of 
the real knowledge of it itself; and whoever has not got the 
System does not know this articulation, for the way or form 
of knowing it is System, and that only. | 

J. W. Wirth‘ makes the axiom of Totality: ‘ Strive to bring 
all your knowledge to the unity of Totality,’ co-ordinate with 
the axioms of Identity and of Sufficient Reason. The logical 
postulate of the systematic combination of our knowledge may 
be very suitably brought to the form of a law of thought, but 
its reference to objective reality should be made more distinctly 
prominent. 

The theory of Division and of Proof is often discussed 
in Systematic or in Methodology, and this is not inadmis- 
sible; but it appeared more convenient to treat of the former 
under the doctrine of the notion, and of the latter under the 
doctrine of inference. This double possibility arises from the 
relativity ofthe notion of Totality, and the corresponding 
relativity of the notion of System. It does not alter the logical 
principle, however. 

' Ueber den Real-Idealismus, in Fichte’s Zeitschrift, N.S., xli. pt. ii. 
196, Halle, 1862. 











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542 § 139. Zhe Principle. 





— 


$ 139. The unity of a system is determined by this, 
that all the individuals contained in it depend on common 
principles. A Principle is an absolutely or relatively 
original element on which a series of other elements 
depends. 

A principle of knowledge (principium cognoscendi) is 
the common starting-point of a series of cognitions—viz. 
the formal and real fundamental intuitions, the funda- 
mental notions and ideas, axioms and postulates. 

A real principle (principium essendi aut fiendi) is 
the common basis of a series of real essences or pro- 
cesses. | 

The principles of knowledge are of two kinds, accord- 
ing as the individual or particular, or the universal, 


The former 


do not correspond to the real principles, but form the 


serves as the starting-point of knowledge. 


natural foundations of propaedeutic knowledge; the 
latter distinctly correspond to real principles and, 
accordingly, form the foundations of strictly scientific 
knowledge. 

The propaedeutic or method of investigation proceeds 
regressively or ANALYTICALLY to the knowledge of real 
principles; the purely scientific or constructive method 
proceeds progressively ΟἹ SYNTHETICALLY from principles 
to particulars or individuals. But it is by no means 
always desirable, in an exposition of the sciences, to 
thoroughly separate the analytic from the_ synthetic 
elements. Both are often to be combined with each 
other in the treatment of individual problems. 


Plato enunciated the logical doctrine that all scientific know- 
ledge rests on principles, and described more closely the double 


Analysis and Synthesis. 543 








way to and from principles. Philosophy shows itself to have a 
higher value than the mathematical sciences, because it alone 
has raised itself to true principles (ἀρχαί), and from these prin- 
ciples descends in pure notions to the less universal, while 
mathematics deduces its individual theorems from assumptions 
(ὑποθέσει5) only, which are not the highest axioms.! 

Aristotle says :? eb yap καὶ ἸΪλάτων ἠπόρει τοῦτο καὶ ἐζήτει, 
πότερον ἀπὸ τῶν ἀρχῶν ἢ ἐπὶ τὰς ἀρχάς ἐστιν ἡ ὁδὸς, ὥσπερ ἐν 
Like 
Plato, he ascribes this double problem to our thinking in 
general: We must ascend from individuals and _ particulars 
which lie nearer the senses, and are therefore the earlier and 
better known for us, to the universals which are the earlier and 
the better known in themselves, in order from them, as a funda- 
mental basis, to recognise what is particular and individual as 


~ ’ > \ a > a \ \ 
τῷ σταδίῳ ἀπὸ τῶν ἀθλοθετῶν ἐπὶ τὸ πέρας ἢ ἀνάπαλιν. 


their necessary consequences : πρότερα δ᾽ ἐστὶ καὶ γνωριμώτερα 
διχῶς "----᾿λέγω δὲ πρὸς ἡμᾶς μὲν πρότερα καὶ γνωριμώτερα τὰ 
ἐγγύτερον τῆς αἰσθήσεως, ἁπλῶς δὲ πρότερα καὶ γνωριμώτερα τὰ 
ποῤῥώτερον "---ἐκ πρώτων δ᾽ ἐστὶ τὸ ἐξ ἀρχῶν οἰκείων" ταὐτὸ γὰρ 
λέγω πρῶτον καὶ ἀρχήν ἁπλῶς μὲν οὖν βέλτιον τὸ διὰ τῶν 
προτέρων τὰ ὕστερα πειρᾶσθαι γνωρίξειν, ἐπιστημονικώτερον γὰρ 
τὸ τοιοῦτόν ἐστιν" οὐ μὴν ἀλλὰ πρὸς τοὺς ἀδυνατοῦντας γνωρίζειν 
διὰ τῶν τοιούτων ἀναγκαῖον ἴσως διὰ τῶν ἐκείνοις γνωρίμων ποιεῖσ-- 
θαι τὸν λόγον. Aristotle gives as an example, on the one hand, 
the sensible intuition of body, and the abstractions of surface 
line and point; on the other hand, the scientific knowledge of 
body from the geometrical elements :° ἡ yap μάθησις οὕτω 
γίνεται πᾶσι διὰ τῶν ἧττον γνωρίμων φύσει εἰς τὰ γνώριμα 
μᾶλλον" καὶ τοῦτο ἔργον ἐστίν, ὥσπερ ἐν Tals πράξεσι τὸ ποιῆσαι 
ἐκ τῶν ἑκάστῳ ἀγαθῶν τὰ ὅλως ἀγαθὰ ἑκάστῳ ἀγαθά, οὕτως ἐκ 
τῶν αὐτῷ γνωριμωτέρων τὰ τῇ φύσει γνώριμα αὐτῷ γνώριμα. 
The author of the second book of the Metaphysics® explains 
this Aristotelian thought by the Platonic image,’ that the eye 


' De Rep. vi. 510 sq.; vii. 533; cf. Phaedr. p. 265; cf. above, 
§§ 14, 134. 

2 Ethic. Nicom. i. 2. 

* Top. vi. 4, 141 5, 15. 

6 Met. ii. (a), 1. 


3 Analyt. Post. i. 2. 
5 Metaph. vii. 4, $ 2 sqq. ed. Schw. 
7 De Repub. vii. init. 








544 δ 139. The Principle. 





of our reason dwells originally only in the dim twilight of the 
sense-world until, trained by exercise, it is able to enter and 
participate in the bright daylight of the realm of pure thought. 
But there is an FORST äne between the Platonic and 
the Aristotelian doctrines when the two methods are defined 
more distinctly. Plato rather requires an ascent to the general 
notion by means of abstraction, and a descent to the more 
special notion by means of division; while Aristotle finds this 
to be a particular instance of the double method of forming 
inferences—the inductive, which conducts to a knowledge of 
the universal, and the sy llogistic, which, by means of its middle 
notion, derives the particular from the universal with apodictie 
certainty. The (Platonic) method of division is only an insig- 
nificant part of syllogistic procedure :' ὅτι δ᾽ ἡ διὰ τῶν γενῶν 
διαίρεσις μικρόν τι μύριόν ἐστι τῆς εἰρημένης μεθόδου, ῥάδιον ἰδεῖν' 

ἐστὶ γὰρ ἡ διαίρεσις οἷον ἀσθενὴς συλλογισμός" ὃ μὲν γὰρ δεῖ 
δεῖξαι, αἰτεῖται; συλλογίζεται δ᾽ ἀεί τι τῶν ἄνωθεν.".----οὐδαμοῦ γὰρ 
ἀνώγκη γίνεται τὸ πρᾶγμα ἐκεῖνο εἶναι τωνδὶ ὄτων. This charge 
against the Platonic method of division holds good only in so 
far as this method is synthetic. But division cannot be subor- 
dinated as a μικρὸν μόριον under syllogistic procedure; it must 
take its place beside syllogism as an equally valid form of 
thought and knowledge of independent value. 

Aristotle calls the reduction of given concrete products to their 
principal elements a solution or analysis, ἀναλύειν, and he 
was accustomed to cite his logical work itself, because it was 
a scientific reduction of thinking, and especially of the differ- 
ent modes of inference, under the title of Analytic. 

Alexander of Aphrodisias® says, in harmony with this use of 
Aristotle: ἀναλυτικὰ δὲ, ὅτε ἡ παντὸς συνθέτου εἰς τὰ ἐξ ὧν ἡ 
σύνθεσις αὐτοῦ ἀναγωγὴ ἀνάλυσις καλεῖται ὕπαρ. μὲν γὰρ σύνθεσις 
ἀπὸ τῶν ἀρχῶν ὁδός ἐστιν ἐπὶ τὰ ἐκ τῶν ἀρχῶν, ἡ δὲ ἀνάλυσις 
ἐπανοδός ἐστιν ἐπὶ τὰς ἀρχὰς ἀπὸ τοῦ τέλους. 

Philoponus° directs attention to the use of the terms analysis 


1 Anal. Pri. i. 31. 
3 Eth. Nic. ii. 5; Anal. Pri. j 
5 Ad Anal. Pri. f. ἃ a. 


2 Anal. Post. ii. 5 
* Cf. above, pp. 6 6 25. 
6 Ad Anal. Post. f. 


Analysıs and Synthesis. 545 





— 


and synthesis’in Geometry. Analysis means finding reasons 
for a given theorem; Synthesis is the opposite procedure.! 

Melanchthon says: ‘ Geometris usitata nomina sunt et no- 
tissima: compositio Synthesis, quae ἃ priori procedit ; e contra 
resolutio seu Analysis, quae ἃ posteriori ad principia regre- 
ditur.’ 

The terms Analysis and Synthesis have been used in Logic 
since the time of Des Cartes? to denote reduction to principles 
and derivation from principles. 

Newton says (at the conclusion of his Optics) the analytical 
must always precede the synthetical in mathematical and 
physical investigation. Methodus analytica est: experimenta 
capere, phenomena observare, indeque conclusiones generales 
inductione inferre, nec ex adverso ullas objectiones admittere, 
nisi quae vel ab experimentis vel ab aliis certis veritatibus de- 
sumantur. Hac analysi licebit ex rebus compositis ratioci- 
natione colligere simplices, ex motibus vires moventes et in 
universum ex effectis causas ex causis particularibus generales, 
donee ad generalissimas tandem sit deventum. Synthetica 
methodus est: causas investigatas et comprobatas assumere 
pro principlis eorumque ope explicare phenomena ex iisdem 
orta, istasque explicationes comprobare. 

Wolff, following the Cartesian definitions, says:? ordo, quo 
utimur in tradendis dogmatis, dicitur methodus; appellatur 
autem methodus analytica, qua veritates ita proponuntur, prout 
vel inventae fuerunt, vel minimum inveniri potuerunt; me- 
thodus e contrario synthetica appellatur, qua veritates ita pro- 
ponuntur, prout una ex altera facilius intelligi et demonstrari 
potest; methodus mixta est, quae ex utriusque combinatione 
resultat. This distinction of the methods is not good as a 
definition, because it gives the derivative and not the funda- 
mentally essential characteristics. 


! Galen also speaks of geometrical Analytic, probably in the sense 
of Logic expounded according to geometrical methods. He mentions 
in his De Propr. Libr. xvi. a treatise of his entitled: dre ἡ γεωμετρικὴ 
ἀναλυτικὴ ἀμείνων τῆς τῶν Στωϊκῶν ὑπόμνημα ἕν. 

? Cf. above, ὃ 24. 3 Log. § 885. 

NN 

















546 § 139. The Principle. Analysis and Synthesis. 





Kant distinguishes analytic from synthetic Judgments,! but 
prefers to apply to Method the terms regressive and progressive 
(methodus regrediens a principiatis ad principia, methodus 
progrediens a principiis ad principiata).? 

Hegel? assumes that both methods are true in the positive 
sciences only because the knowledge conveyed in them relates 
only to the ‘understanding,’ and is only finite knowledge, 
The method of philosophical speculation is Dialectic, the form 
of the ‘ Absolute Idea,’ of the ‘ pure reason.’ But this Dialectic 
is only the supposititious attempt at a synthesis, which does not 
yield the results of Analysis. 

Schleiermacher requires‘ that the ‘ process of deduction’ 
should rest upon a ‘ process of induction’ (and Synthesis upon 
Analysis). 

Trendelenburg,’ avoiding both an exclusive empiricism and 
the Hegelian .theory of ‘ pure thinking,’ sees synthesis to be 
the glory of the sciences, but recognises that the condition of 
the scientific character of synthesis is its subjection to the 
strict discipline of the analytic methods. | 

Beneke® proves how synthesis in all the sciences, mathe- 
matics not excepted, is conditioned by previous analysis, and 
warns us against betaking ourselves to syntheses ἃ priori, 
which, because they are knowledge without foundation, are no 
better than caprice and fancy. 

The following remark will suffice upon the present mathe- 
matical use of the expressions Analysis and Synthesis. Con- 
structive Geometry usually takes the synthetic course of proof, 


and leaves the analytic methods to find proofs in solutions of 
problems. However, Geometry, which reckons on the basis of 
the systems of co-ordinates, proceeds, by way of preference, 
analytically, when it regressively seeks the conditions under 
which certain equivalents are satisfied. It proceeds by means 
of algebraical analysis which rests also on this regressive pro- 
cedure, and is therefore called Analytical Geometry. 


1 Cf. above, § 83. 2 Logik, § 117. 
3 Encycl. § 226 ff. 4 Dial. ὃ 283. 
5 Log. Unters. 2nd ed. ii. 294, 6 Log. ii. pp. 159-188. 


§ 140. The Analytic (or Regressive) Method. 547 





§ 140. The empirical data, from which all scientific 
investigation in its regressive or analytical part (or 
inductive investigation in the wider use of the expres- 
sion) must start, are given immediately by external 
and internal Perception (perceptio), and mediately by 
Testimony (testimonium ). 

Perception when animated by a conscious aim becomes 
Observation (observatio), and when the object admits 
of the investigation, Hxperiment (experimentum). In 
experiment we ourselves change the conditions of what 
happens; we seek to know what conditions are influential 
and the kind of influence they possess expressly for the 
sake of the observation, and the answer to the question 
stated is given by Nature herself. 

The trustworthiness (fides) of testimony is settled by 
the general logical rules which govern the inference from 
the conditioned to the condition, and, more particularly, 
the construction and verification of hypotheses (§ 134), 
for this is only a special case of that more general class. 
The fact to be concluded is the real prius of the testi- 
mony. The content of the testimony may have for its 
ground, either that the event has happened and has been 
observed exactly in the same way, or that the obser- 
vation has been influenced by a false apprehension, 
an untrue recollection, preference of some fancy to 
strict accuracy, or the confusion of subjective judgment 
with objective fact. But the witness of an immediate 
or eyewitness (testis primitivus, proximus, oculatus), 
who is an immediate witness notoriously or according 
to the assured concurrence of historical criticism, is 


NN 2 








es ee 























548 § 140. The Analytic (or Regressive) Method. 





trustworthy, provided that he has been able to appre- 
hend the fact strictly and truly, according to his intel- 
lectual and moral condition, and to represent it truly, 
and has taken care to do so. The agreement of several 
immediate witnesses with each gives to their assertion 
a very high probability, if it is proved that they are 
independent, that they have not been deceived by the 
same deception, nor have been affeeted and psycho- 
logically influenced by the same one-sidedness in appre- 
hension and statement; for a purely accidental agree- 
ment in an accidental circumstance has, according to 
the laws of the calculation of probability (cf. $ 132), a 
very high degree of probability in all complicated rela- 
tions. The trustworthiness of mediate witnesses (testes 
secundarii, ex aliis testibus pendentes) is determined 


partly by their sense and critical capacity, partly and. 


chiefly by their relation to immediate witnesses. It is 
an essential problem, but seldom absolutely soluble, to 
discover the genealogy of testimony. The testimony 
of later witnesses is suspicious, especially when there is 
anything in it to serve a distinct (poetical, national, 
philosophical, dogmatic, or practical) tendency, and the 
further it stands from the actual occurrences. The 
verification of the subjective trustworthiness of different 
witnesses is reciprocally related to the verification of 
the objective probability, which what is attested has in 
itself and in connection with undoubted facts. Criti- 
cism is positive, so far as it has to construct a com- 
plete picture of the real previous occurrence, by com- 
bining the true elements and excluding the false. 

The regressive or analytical investigation seeks to 


§ 140. The Analytic (or Regressive) Method. 549 


recognise real principles on the basis of admissible 
facts. Its knowledge is either given to it in perception 
as such, or is innate in the subject in such a way that it 
is brought into consciousness by progressive development 
—not that it is ascertained by an immediate intuition 
of reason, but that it is obtained from the given content 
of perception by a thanking objectively conditioned. This 
thinking fashions the material of perception, not (as an 
artist does a block of marble) according to forms, which 
are in themselves foreign to it, but (as nature does the 
living germ) according to the relations given in itself 
and conditioned by the forms of the objective reality. 
In reference to this material element, the proposition is 
true: ‘ nihil est in intellectu, quod non fuerit in sensu;’ 
but the fashioning of the material of (external and in- 
ternal) perception in thinking is not an operation of less 
value, it is the more essential side of the process of 





knowledge. 

Abstraction leads to the most general notions of prin- 
ciple significance. Abstraction, in conjunction with 
the idealising activity passing beyond what is given, 
fashions what is the higher in science according to scien- 
tific laws (as in art according to aesthetic laws), into 
the Idea (idea in the subjective sense) or into the regu- 
lative (typical) notions. 

Judgments which contain scientific axioms of value as 
principles (axiomata) are framed partly analytically, 
partly synthetically. The former (e.g. the arithmetical 
axioms) originate by the. resolution (analysis) of intui- 
tions or notions present before the mind, and have 
immediate evidence independent of experience. The 














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550 $ 140. The Analytic (or Regressive) Method. 


latter (e.g. axioms of geometry and the postulates, which 
are only another form of axioms, and which assert the 
possibility of doing what is required) depend partly on 
Induction and Analogy, partly on idealisation and hy- 
pothetical assertion, accompanied by the verification of 
the truth of the hypothesis in its consequences, 
which leads to a successive exclusion of the false (by 
means of indirect proof) and the confirmation of what 
is true. In complicated problems the first attempts at 
hypotheses must not include the whole problem. As 
many fixed starting points as possible must first be 
gained inductively and by means of special hypotheses 
and their verification, in order thereby to settle the 
principal question. Every principle, if it contains 
hypothetical elements, must be verified in its conse- 
quences, and hence it is possible to decide between con- 
tradictory elements in this way, that each shows its true 
character in its theoretical and practical consequences. 
The axiom: ‘contra negantem principia non est dis- 
putandum,’ is false and inhuman. In anormal develop- 
ment in knowledge, as in life, the lower element is 
overcome by the higher, and contradictory principles 
equally justifiable find their true place of union in a 
common higher principle. 





There is no need for a special ‘ ars inveniendi’ or “ Topic, 
co-ordinate Logic as the ‘ ars judicandi,’ such as Christian Wolff 
and other logicians, following the view of Leibniz, have desired. 
The analytical method which employs the modes of knowledge 
explained above in detail, the product of perceptions, intuitions, 
notions, judgments, inductions, &c. is the true art of invention, 
and so is the synthetic method from its own side. Topic can 
only be divorced from Logic when used in the service of Rhe- 


δ 140. The Analytıc (or Regressive) Method. 551 





toric. Zrendelenburg says very truly:' Disputation or Logic 
should abolish the chapter De Inventione. When the laws of 
Logic are once founded on the basis of the individual sciences, 
they will become much better able to guide one in discovery 
than could have been the case by means of the previous abstract 
treatment, whether conducted in the interest of rhetoric or of 
science. 

The true apprehension uf facts, free from any individual and 
subjective confusion, is a work of education. The teacher, 
physician, historian and judge, have daily occasion to observe 
how little men are accustomed to describe the simple facts, and 
how very much they mix up in the statement (unconsciously 
and unintentionally) their own opinions and interests. “ It is 
inconceivably hard, I had almost said impossible, to describe 
what has been seen or heard wholly and exactly as it has been 
seen and heard. We often introduce our own feelings without 
anticipating it, and although we have the strongest and purest 
love of truth’? ‘We see in the descriptions not the things 
themselves, but only the impressions which they have made 
upon the soul of our author, and we know that the account of 
the impression never fully corresponds to the things. It is the 
business of the historical critic to infer back from the narrative 
to the first form of the impression, and from this to the actual 
fact, to remove the additions and changes due to subjective 
influence, and to restore the objective occurrence.’? 

The task of the regressive (ἃ potiori inductive) investigation 
consists in starting from ascertained individuals, and in ex- 
plaining everything that follows, where premises are gained 
sufficient to prove the truth as accurately as possible. The 
result again serves as a premise for further argumentation, so 
that, so far as this arrangement goes, all other points of view 
are noticed only in so far as the final purpose, which consists 


| Erläut. zu den Elem. der Arist. Log. p. viil. 

2 Schiller in Caroline von Wolzogen, Schiller’s Leben, ii. 206, 
1830. 

3 Heinr. von Sybel, Ueber die Gesetze der Historischen Wissens, p. 
12 f.: Bonn, 1864. 




















552 § 140. The Analytic (or Regressive) Method. 





in the attainment of the greatest certainty possible, allows 
free play to each. After that a series of individuals has 
been thoroughly established in this way, the first thing to be 
done is to settle what the principles are. When full certainty 
cannot be attained, the degrees of probability are to be dis- 
covered and denoted with as much accuracy as possible.! 
These postulates are equally true for the sciences of Nature 
and of mental life. K. O. Müller, looking upon them as 
elements of method common to history and the natural sciences, 
designates them: a quick observation of the events of what is 
given in experience, the collection of as many individual points 
as it is possible to find, the enquiry into their regular concatena- 
tion according to the laws of probability, and their reference 
to the given fundamental elements of the universe of nature. 
The investigation of individuals gains in significance as it 
can insert itself as a moment in the sum total of the scientific 
labour. Advance in the higher grades of knowledge is not to 
be made by means of a crude independence, which, trusting to 


common sense or guided by the idle fancy of personal genius, 


for the sake of a supposititious ‘freedom from prejudice’—which 
is often only an unscientific persistence in superficial opinions, 
and full of unripe conceits—despises the study of the investiga- 
tions of others, or contents itself with half and half apprehension 
without thorough-going reflection and critical accuracy. Nor 
is it attained by a compulsory soulless resignation, which, pro- 
ceeding wholly upon acquired knowledge, and devoted to the 
safe appropriation and faithful reproduction of treasures pro- 
duced by creative spirits, leaves unemployed its own power of 
production. It is attained by reaching an independent insight 
from the basis of the most accurate acquaintance with the 
whole development of the science up to this time. In science 
man, starting from the natural condition of freedom from re- 
straint, must reach true freedom by submission. 

The speculative instinct aims at the most general principles, 
and anticipates them in poetical or half-poetical forms before 


1 Cf. the remarks on method in my Platonischen Untersuchungen, 
pp. 99, 112, and 268: Wien, 1861. 


S141. The Synthetic (or Constructive) Method. 553 


N 








striet science is able to recognise them. Exact investigation 
contents itself with the inductive discovery and verification of 
merely empirical laws, while the first principles cannot be 
established on the basis of facts with striet accuracy, but is 
too ready to sacrifice depth to certainty. The highest problem 
is to attain the end, pointed out by speculation, by the methods 
of exact investigation. Bunsen calls this, more immediately 
with reference to the Philosophy of History, the ‘ union of the 
spirit of the Baconian system with the categories of the Ger- 


man speculative mental Philosophy.’ ! 
What may be said upon the history of the doctrines of 


Empiricism, Rationalism, Critical Philosophy, &c., because it 
must confine itself to the general stand-point of a theory of 
knowledge, belongs to the whole history of Logic as the doc- 
trine of knowledge. We must therefore here refer to our 


historical survey.” 


$ 141. The means which method has at command 
for the constructive or synthetic construction of know- 
ledge are: Definition, Division, and Deduction. 

Definition ensures the permanence of the result of 
the process of abstraction, and serves as a foundation 
for Division and Deduction; and these processes again 
lead to new definitions. 

Division separates the sum total of the scientific 
material, according to the relations of superordination, 
subordination, and co-ordination, in the belief that their 
regular arrangement ensures a true copy of the real 
relations. They are not reduced to a ready-made 
scheme, but the schematism, down to its last sub- 


I Hippol. i. 276; cf. my article Ueber Idealismus, Realismus und 
Ideal-Realismus in Fichte’s Zeitschrift, vol. xxxiv. 63-82, 1859. 

2 Cf. above, §§ 10-35; cf. also expressions in §§ 37; 40; 44; 46 
fi; 51; 56f.; 67; 73; 74 ff; 83; 127; 129; 181; 184 ff; 138 ἢ, 





2 PPS mie eas ο 




















554 § 141. The Synthetic (or Constructive) Method 





divisions, is to represent the essence of the content in 
the form of a natural organisation. The (Kantian) 
principles of homogeneity, specification, and continuity 
are to be applied in definition according to the nature 
of the case, and not as subjective maxims. 

Deduction, leading to the results of the processes of 
Abstraction and Induction, establishes the particular 
and individual by means of the universal. It authen- 
ticates its genetic or teleological necessity in a syllogistic 
form of thought, by means of a combination of series of 
reasonings suitable to the case (method of genetic Ex- 
planation; method of teleological Speculation). Deduc- 
tion can never deduce the reality of the particular and 
individual without the universal, but it can never deduce 
it from the universal alone. 


According as the definition of notions and division or de- 
duction fills the more prominent place in synthetic knowledge, 
Lrendelenburg' distinguishes ‘ Systems of Arrangement’ (classi- 
fications) and ‘ Systems of Development’ (explaining theories). 
The former take the form of descriptive, the latter of explana- 
tory, natural and mental sciences. But since the arrangement 
must as much depend on that concatenation of things which is 
knowable to us, as the possibility of deduction does on the 
notional arrangement, the end of these elements can never be 
wholly separated from the other. Each can attain to scientific 
completion only in and by each other (cf. § 66). 

The more empirical character of a scientific system is caused 
by the more frequent use it makes of the regressive or analy- 
tical method, in so far as it, keeping to what is given, does not 
attempt to reach the absolutely highest principles. Its more 
speculative character is caused by the more frequent use it 
makes of the constructive or synthetic method, in so far as it, 


I Loy. Unters. 2nd ed. ii. 411. 


§ 141. The Synthetic (or Constructive) Method. 555 





starting from first principles, seeks to recognise reality by 
means of a freely-fashioned product of thought in such a way 
that in every extension of what is given the path of thought 
is determined by the aim of knowledge. This opposition is, 
however, relative only. The so-called empirical sciences, if 
they wished to deprive themselves of all the thoughts which 
pass beyond mere experience, would renounce their scientific 
character. And philosophy, if it would not dissolve into airy 
fancy, must assume, in order to the regressive knowledge of 
principles, the whole of the positive sciences. Just as the roof 
or cupola does not rest immediately on the floor, but the floor 
bears it by means of the other parts of the building, so philo- 
sophy rests on an empirical foundation by means of the positive 
sciences. The development of one and the other is always 
reciprocal.’ In all the sciences without exception speculation 
requires the empirically given material, and empiricism requires 
the speculative quickening. Only the relation of these elements 
to each other is different in different sciences. 

Whenever the modifications of the general laws of Logic in 
their application, according to the difference of the content of 
different sciences, come into consideration, it becomes a question 
of PARTICULAR or APPLIED Logic ($ 8), and no longer 
belongs to GENERAL or Pure Locic. When we, starting 
from the facts of self-consciousness in themselves undoubted, 
have found in the gradual transference of the content and forms 
of the mental (psychic) world to the outer world, accomplished 
by means of thinking according to the measure of sense per- 
ception, the course of human knowledge, and from the end 
and aim of knowledge, which is material truth, and which lies 
in the measure of the attainable agreement of the subjective 
picture with the objective reality, have conceived the forms of 
knowledge and the universal laws of their structure and com- 
bination, we stand at the boundaries of our task. 


1 Cf. the author’s article on the Begriff der Philosophie, in Fichte’s 
Zeitschrift, vol. xlii. 185-199, 1863. | 

















APPENDIX A. 


-- τ τοτοΐξοο-“ 


ON RECENT LOGICAL SPECULATION IN ENGLAND. 


$ 1. Tue revival of logical study in England dates from the 
publication of Archbishop Whately’s Elements of Logic. Before the 
appearance of this work, the study of the science had fallen into 
universal neglect. It was scarcely taught in the universities, and 
there was hardly a text-book of any value whatever to be put into the 
hands of the student.’ 

The Elements of Whately was by no means a good text-book. The 
author wrote without having a very extensive knowledge of his subject, 
and did nothing to enlarge the science he professed to teach; but he 
had the great gifts of a clear plain style, good arrangement, and a 
wonderful power of fresh and interesting illustration. The book, 
which had no pretensions to scientific accuracy, was nevertheless so 
successful that probably no text-book on Logic ever went through so 
many editions. It awakened a real study of Logic, and was the fore- 
runner of a host of logical text-books, which, if they added little to the 
science they profess to expound, at least showed the national zeal for 


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a nn re, pel a er green. σ'π 


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i 
& 
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the study. 

$ 2. A more scientific spirit, however, soon showed itself among 
English logicians, and, when it appeared, took a double direction, 
due to its twofold origin. Two influences were working in men’s 
minds, that of Kant and that of Hume. The Kantian influence gave 
us the formal Logic of Hamilton, Mansel, and Thomson; the influence 
of Hume, the Logic of Mill and Bain. 

These two schools, however, do not exhaust the list of scientific 
English logicians. 

Among the formal logicians, the doctrine of a quantified predicate 
became a leading doctrine, and this prepared the way for the mathe- — 
matical Logic of Boole. Among the sensationalist logicians the 





1 Cf. Hamilton’s Discussions, Art. IV. Logic. 











558 Appendix A. 





doctrine of Induction was most Important, and their theories cannot be 
explained without discussing the relative theories of Dr. Whewell. 

We have thus two classes of logicians—Formal and Sensationalist ; 
the former by their doctrine of a quantified predicate inseparably 
related to the mathematical Logic of Boole, and the latter by their 
theory of induction closely allied to the inductive Logic of Whewell. 

§ 3. The Formal Logic of Hamilton, Mansel, and Thomson may 
be traced to a Kantian influence. These logicians expressly say that 
they are indebted to Kant for their whole view of the science. They 
‘have in many instances borrowed their divisions and terminology from 
Kant, and they are to be distinguished from other English logicians by 
strongly asserting the Kantian maxim, that Logic has nothing to do with 
the objects of knowledge, and, therefore, can only be concerned with 
the forms of thought. They push their theory of Formal Logic much 
farther than Kant did, however. Kant was not only a logician but a 
metaphysician, and his logical theories were to a great extent the 
result of his metaphysical enquiries. The ultimate matter of know- 
ledge, things-in-themselves, was wholly unknown. It was only known 
in certain relations, when combined with certain forms which were 
imposed upon it by mind, and by which it was brought into the 
presence of mind. The invariable and permanent part of knowledge, 


i.e. that part of it which could form the material of a strict science, 


was this formal element, and in thinking was the form of thought in 
its various modifications. There was always some degree of coinci- 
dence between Kant’s metaphysical and, his logical doctrines—a 
coincidence which indeed expressed itself in the parallelism which he 
found between the metaphysical and logical categories—and this 
coincidence kept him from pushing his logical theories to their last 
consequences. But our English formal logicians were not held back in 
any such way, and their Logic is a purely formal Logic from beginning 
toend. They begin by stating the incomplete disjunction—Logic has 
nothing to do with the objects of knowledge (or else it could not be 
distinguished from metaphysics, &c.) ; therefore it: must occupy itself 


Appendix A. 559 





in describing the school to which they belong, we may take from each 
that part which he has most carefully elaborated. Dean Mansel has 
marked out the sphere and described the work allotted to formal Logic 
most thoroughly. We must go to Sir W. Hamilton’s writings to find 
how the system is worked out in details. And Archbishop Thomson 
has given us the only thoroughly elaborated representation of the whole 
of formal Logic. His Outlines of the Laws of Thought is a text-book 
for junior students, however, and cannot be taken as a perfect descrip- 
tion of Formal Logic in all its parts. aie | 

§ 4. According to Dean Mansel,' Logic is the science of the formal 
laws of thought, or the science of the laws of thought as thought. Its 
province is both constructive and critical. 

Logic as constructive takes the three formal laws of thought,? and, by 
applying them to the materials from which notions, judgments, and 
reasonings are constructed, frames formally these three products of 
thought. 'The material must be given ere constructive Logic can act. 
In forming notions attributes must be given, in forming judgments 
notions, and in forming reasonings judgments. In the formation of 
notions all that Logic has to do is to see that the attributes out of which 
the notion is to be framed are not logically contradictory the one of 
the other. The material validity is not the question to be considered. 
‘Centaur’ is as correct logically as‘man.’ In forming judgments all 
that Logic is concerned with is to see that the notions put together in 
the judgment are not. self-contradictory. An affirmative judgment is 
true, formally and logically, whenever the given notions have no 
attributes which contradiet each other; a negative judgment is true, 
formally and logically, whenever the given notions contain attributes 
which contradiet each other. In forming a syllogism, Logic has only to 
consider whether the given judgments are free from contradiction, and 
are put together under such conditions of quantity and quality that 
the mere act of thought necessarily elicits the conclusion. It has 
nothing to do with the truth of the premises. ‘Purely formal mediate 
reasoning or syllogism is dependent on the same laws as formal 


nr . 


—— 


= an Nr 


judging, the Law of Identity governing the affirmative categorical 
syllogism, and the Law of Contradiction the negative ; while the sub- 
ordinate Law of Excluded Middle is called into operation in the im- 
mediate inferences of Opposition and Conversion.’* This function of 





exclusively with the form of thought.! The third possibility that Logic 
treats of, the relation of thought to existence, or of the forms of thought 
in their relation to their objects, does not come into their theory of 
Logic, though in their practical illustrations of the science it can scarcely 
be avoided. 1 Mansel’s edition of Aldrich’s Artis Logicae Rudimenta, pref. lvii—lxxvii, Pro- 

The three writers whose names are set at the head of this paragraph, | 
while they must be considered to be thoroughly original and indepen- 
dent thinkers, are yet so far agreed in their views of the science, that, 


legomena Logica, pp. 181-265. 
2 The laws of Identity, Non-Contradiction and Excluded Middle. The law of 


Reason and Consequent, commonly given as the fourth law, is excluded by Mansel 
: and Hamilton. Cf. above, p. 231. 
a 588, * Artis Log. Rud. p. Ἰχχ. 














560 Appendix A. 





—— 


Logic is the same in relation to special classes of these products of 
thought. For example, in Definition, which is a kind of formation of a 
notion, all that Logic has to do is to determine the conceivability of the 
several attributes contained in a given notion by their analysis and 
separate exposition. If the attributes are compatible the definition is 
logically valid. On the other hand, Logic as critical examines whether 
notions, judgments, or reasonings are framed in accordance with the 
laws of thought. It adequately determines the conceivability of a notion, 
the truth or falsehood of an analytical judgment, or the validity of a 
professedly fo:mal reasoning. It cannot determine the real correctness 
of the notion, the truth or falsehood of a synthetical judgment, or the 
validity of a reasoning professedly material. 

Such a view of the nature and province of Logic makes it differ 
widely from the Logic of Bacon, and indeed from any pre-Kantian 
Logic whatever ; and any attempt to combine under the one name of 
Logic a Baconian theory of evidence and the description and application 
of the laws of pure thought cannot but be distasteful to its advocates. 
Accordingly, Dean Mansel elaborately protests against any such com- 
bination. The two disciplines, he contends, are entirely distinct. They 
differ in the object they treat of, in the nature of the laws they con- 
sider, in the conceptions they imply, in the methods they involve, and 
they use common terms in the most widely different senses.! 

In short, the distinction between the forms of thought and the objects 
thought about is pushed to such a length that it becomes forced and 
unnatural. The vital and important thing. in all knowledge, and the 
real question to be settled in any theory of knowledge, the relations of 
thought to the things thought about, is entirely passed over. And we 
have an elaborate framework of artificial mechanism instead of the 
representation of the ways in which the mind works in the attainment 
of knowledge. 

§ 5. It is evident that when Logic becomes only a statement of the 
fundamental laws of thought ‘with a postulate, and the application of 
these laws to things thought about, the science becomes much more 
simple and mechanical than Aristotle, or any other logician who 
believed Logic to be a theory of knowledge, had ever imagined, and a 
New Analytic is required to supersede the Old. This New Analytic has 
never, unfortunately, been worked out to completeness ;? but we know 


1 Cf. Artis Log. Rud. Pref. Ixxiii.; cf. Hamilton’s Lect. on Logic, ii. 229 ff. 

2 The completest account given is to be found in An Essay on the New Analytic 
of Logical Forms, &c., by Professor Thomas Spencer Baynes, of St. Andrews. 
Scattered notices of the New Analytic are given in the Appendix to Sir W. Hamil- 
ton’s Lectures. 


The New Analytic of Logical Forms. 561 





enough about it to be able to describe it, and also to see how it led, by 
a strange ‘ irony of fate,’ when we think of the opinions Hamilton held 
about mathematics and mechanics, to the mathematical Logic of Prof. 
Boole and to the mechanical Logic of Prof. W. Stanley Jevons. 

$ 6. According to Sir W. Hamilton, the NEw Anatytic or LoGIcAL 
Fors (1) shows that the distinction between (metaphysical) whole of 
Comprehension and (logical) whole of Extension runs through all Logic, 
and gives it another side which has not been recognised; (2) tho- 
roughly enforces the postulate of Legic, and thereby effects numerous 
simplifications and changes in the science ; and (3) constructs a scheme 
of Symbolical Notation which will display, with mechanical simplicity, 
jropositional and syllogistic forms in all their old and new appli- 
cations.! 

§ 7. I. A notion has both comprehension and extension ; it connotes 
a certain number or whole of attributes, and denotes a certain number 
or whole of objects. ‘Thus ‘man’ stands for either the sum total of 
the attributes which make the meaning of the notion, or the sum total 
of the objects to which the notion may be applied. Unless this double 
reference be explicitly enounced, the notion is ambiguous. ‘Therefore 
in propositions and in syllogisms we must make it clear whether we are 
speaking of the comprehension or of the extension. This is best done 
by explicitly stating what the ambiguous copula ‘is’ means. In the 
sphere of Comprehension is means comprehends in; man is mortal 
means: the notion man comprehends in it the notion mortal. In the 
sphere of Extension is means 18 contained under ; man is mortal means: 
the notion man is contained under the notion mortal. Now as the two 
wholes of Extension and Comprehension are always in the inverse ratio 
of each other, what is smaller in extent is larger in content. When we 
say ‘man comprehends mortal,’ the notion man, the subject, taken in 
comprehension, is the greater, and the notion mortal, the predicate, is 
the less; but when we say ‘ man is contained under mortal,’ the notion 
mortal, the predicate, taken in extension, is the greater, and the notion 
man, the subject, is the less. The subject and predicate, which are 
related to each other as contained part and containing whole in Exten- 
sion, change places, and become comprehending whole and compre- 
hended part in Comprehension. This reciprocal relation must be 
noticed, or ambiguity will result. There must therefore be Compre- 
hensive as well as Extensive syllogisms, and the comprehensive syllo- 
gism may, in each case, be formed from the extensive by changing the 
meaning of the copula in the propositions and transposing the pre- 
mises, 

1 Leet, on Logie, p. 250. 


0 0 


ethene 


= eS a ee 
a uw weg rere . > 
x 














562 Appendix A. 





This addition of comprehensive judgments and inferences does not 


recommend itself. The terms ‘ whole of comprehensien’ and ‘ whole of 


extension,’ when applied to notions, are to a certain extent misleading; 
the words ‘ connotation’ and ‘ denotation’ better express the relations. 
Denotation is a quantitative relation; it means ability to denote ἃ 
greater or smaller number of objects; and when we use ‘man’ de- 
notatively, we can say with correctness ‘some men’ or ‘all men. 
‘ Man’ is then a whole and has parts. But Connotation is a qualitative 
relation; it means ability to represent certain qualities; and when we 
use ‘man’ connotatively we cannot say with correctness ‘some man’ or 
‘all man.’ ‘Man is not a whole that can so be divided. The term 
‘comprehensive’ is still more unfortunate when applied to judgments. 
ii is absurd to say, ‘Some men are black-haired,’ meaning that some 
part of the whole of the attributes comprehended under the notion man 
comprehend the notion black-haired. We may say, the attributes con- 
noted by ‘man’ are sometimes accompanied by the attributes con- 
noted by the notion ‘black-haired,’ but this is not a judgment in 
Comprehension. The truth is that a judgment does not naturally take 
this double quantity of comprehension and extension. The subject of 
a judgment is naturally denotative; it denotes an object or objects. 
While the predicate of a judgment is naturally connotative ; it connotes 
an attribute or attributes (cf. App. B). The same remarks apply to 
Syllogisms in Comprehension.! 

ὃ 8. II. The postulate of Logic is—To state explicitiy what is thought 
implieitly2 The chief result which conies from the rigid enforcement 
of this postulate, is: that logically we take into account the quantity 
always understood in thought, but usually, and for manifest reasons 
elided in its expression, not only of the subject, but also of the pre- 
dicate. On this quantification of the predicate the principal changes of 
the New Analytic are based.? 

1. The preindesignate terms of a proposition, whether subject or 
predicate, are never to be thought as indefinite (or indeterminate) in 
quantity. All or some or an equivalent predesignation must be pre- 
fixed to each term.* 

2. A proposition becomes an equation. This conception of the 
nature ef a proposition, though given by Hamilton as a result of the 
application of the quantification of the predicate, is perhaps rather its 


1 Cf. also Mill, Exam. of Sir W. Hamilion’s Phil. 3rd ed. p. 488 ff. 

2 This single postulate is elaborated into five rules by Sir Wm. Hamilton ; cf. 
Lect. on Log. ii. 252. It is stated variously ; ef. Bayne’s New Analytic of Logict! 
Forms, p. 4. 


® Lect. on Log. ii. 250. ı Cf. Bayne’s New Analytic, p. 5 fl. 


The New Analytic of Logical Forms. 563 





cause. For whenever the relation of subject and predicate in a pro- 
position is thought to be, not that of subsistence and inherence or of 
object and attribute inhering in it, but an equation, we must think 
the predicate as a quantity which is equal to the subject, and we must 
think it as quantified, and so exactly correspondent to the subject. 

3, Whenever a proposition is conceived to be an equation, and the 
copula is seen to be equivalent to the sign of equality (=) it is evident 
that there can no longer be three species of Conversion, but only one— 
that of Simple Conversion (All a=some B, is the same as: some B= 
all a).! 

4. Whenever propositions are seen to be equations, inference is 
greatly simplified. Categorical syllogism is simply the comparison of 
equal sides of equations, ‘ it is the product of that act of mediate com- 
parison, by which we recognise that two notions stand to each other 
in the relation of whole and part, through the recognition that these 
notions severally stand in the same relation to a third ;’ and its general 
laws may very well be gathered into one canon which will guide this 
comparison. The canon is: ‘ What worse relation of subject and pre- 
dicate subsists between either of two terms and a common third term, 
with which both are related, and one at least positively so—that rela- 
tion subsists between these two terms themselves.’ ? 

5. From this one canon all the species and varieties of Syllogism 
may be evolved. 

(1) There are two kinds of Syllogism corresponding to the two kinds 
of logical wholes and parts. ‘These wholes are comprehensive and ex- 
tensive. Hence there are syllogisms of comprehension and extension. 
The first clause of the canon—‘ What worse relation of subject and pre- 
dicate subsists between two terms, &c., determines these different kinds 
of syllogism. In the whole of comprehension the predicate is part of 
the subject, and therefore is worse than the subject. In the whole of 
extension the subject is part of, and therefore worse than the predicate. 

(2) Syllogisms vary in relation to Figure and Mood. 

(a) The variation of Figure arises from the various positions of the 
middle term in relation to the extremes, and this is evidently deter- 
mined by the clause—‘ What relation subsists betwee. either of two terms 
and a common third term.’ 

(b) The variation of Mood arises from the various quantity and 
quality of the propositions which make the Syllogism, and this variety 
is determined by the clause—‘ What worse relation of subject and pre 


' Hamilton’s Lect. on Log. ii. 271 ff.; Baynes’ New Analytic, p. 21 ff. 
? Cf. Baynes’ New Analytic, p. 53 ff. 
* Ibid, pp. 56, 57. 

00 2 











564 Appendix A. 





dicate, &c. A particular quantity is a worse relation than a universal. 
and a negative quality a worse relation than a positive.! 

6. Logicians have laid down special laws of Syllogism which regulate 
the inferences in the various Figures. All of them emerge on the 
neglect to give the predicate explicitly the quantity which implicitly 
belongs to it, and all of them are rendered useless and most of them 
false as soon as the quantification of the predicate takes effect. The 
enunciation of the one supreme canon of Syllogism therefore abrogates 
these special laws.” 

7. The supreme canon of categorical Syllogism, since it determines 
all the varieties of Syllogism, will determine the number of syllogistic 
Figures. A reference to this canon demonstrates the exclusive pos- 
sibility of Three Syllogistic Figures, and abolishes the so-called Fourth 
Figure. The clause which determines the variations of Syllogism 
with respect to Figure is—‘ What worse relation of subject and 
predicate subsists between either of two terms and a common third 
term,’ &c., and this clause determines all the variations possible. 
These are three: for there are only three varieties of relation. The 
relations are :— 

(1) That in which the common third term is subject of one of the 
terms, and the predicate of the other. This gives the First Figure in 
Extension and in Comprehension. For example :— | 

In Comprehension 

S comprehends M ; 

M comprehends P : 
.. S comprehends P. 


In Extension 
M is contained under P ; 
S is contained under M: 
.*, S is contained under FP. 


(2) That in which the common third term is predicate of both the 


other terms. This gives the Second Figure, which admits affirmative 


as well as negative conclusions. For example :— 
Negative 
All P is all M; 
No S is any M: 
. No S is any P. 


Affirmative 
All P is all M; 
All S is some M: 
„. All S is some P. 


(3) That in which the common third term is subject of both the other 
terms. This gives the Third Figure, which admits of universal as well 


as of particular conclusions. For example :— 


Partieular 
AlMisallP; 
Some M is some S: 

ἡ, Some S is some P. 


Universal 
All M is some P; 
All MisallS: 
+, All S is some P. 


1 Baynes’ New Analytic, p. 74. 2 Cf. Hamilton’s Lect. on Leg. pp. 285, 345, 90 


The New Analytic of Logical Forms. 565 





The so-called Fourth Figure is a hybrid. Its premises proceed in 
the whole of Comprehension. For example :— 


All PisM ; All P comprehends M ; 
AllM is 8S: All M comprehends 8: 
.. Some SisP; „Some Siscontained under P; 


which being inter- 
preted gives 


ie. in the premises the two subjects P and M are greater than the two 
predicates M and S, while in the conclusion the predicate P is greater 
than the subject S. This Figure is also useless, for reasoning is scien- 
tifically complete without it.! 

8. Since Syllogism is the result of an act of immediate comparison by 
which we recognise that two notions stand to each other in the relation 
of whole and part, through the recognition that these notions severally 
stand in the same relation to a common third notion, it is not necessary 
that these notions stand to each other in the relation of subject and 
predicate. And since the syllogistic variation of Figure depends on the 
varieties of the relations of subject and predicate, Syllogistic Figure is 
not an essential variation. 'There may be Unfigured as well as Figured 
Syllogism. 

The Unrigurep SYLLocısMm is that in which the terms compared do 
not stand to each other in the reciprocal relation of subject and predi- 
cate ;? the Figurep SyYLLosısm, that in which the terms compared have 
this relation. But if Figure itself be only an accidental variation of 
Syllogism, one of the Figures, the first, cannot be in itself the only 
true and valid form of syllogistic inference, and it is absurd to reduce 
the others to that form in order to show their validity. Hence the 
New Analytic abolishes Reduction. 

9. But if Reduction be unnecessary, each Figure must have an 
organic principle of its own on which it proceeds, and, since all varie- 
ties of syllogism are to be evolved from its supreme canon, these canons 
of the separate Figures are to be evolved from that supreme canon. 
And since the variation of Figure is determined by the varieties of rela- 
tion of the extremes with the common third term implicitly given in 
the supreme canon, the canons of each of the Figures will be formed by 
explicitly enouncing that particular variety of relation which deter- 
mines each Figure. 

In the First Figure the common third term is the subject of the one of 
the terms and the predicate of the other. Hence the canon of this Figure 
will be: What worse relation of determining (predicate), and of deter- 


ı Cf. Baynes’ New Analytic, pp. 65-69. 
2 Cf. above, p. 376. 
8 Cf. Baynes’ New Analytic, p. 153 ; Hamilton’s Lect. ii. 404, 














566 Appendix A. 





mined (subject), is held by either of two notions to a third, with whic} 
one at least is positively related; that relation do they Fe 
(directly) hold to each other, and indirectly (mediately) its converse : 

In the Second Figure, the common third term is the predicate of both 
of the other terms. Hence the canon of this Figure will be: Wha 
worse relation of determined (subject) is held by either of two notions to a 
third, with which one at least is positively related ; that relation do 
they hold indifferently to each other. 

In the Third Figure, the common third term is the subject of both of 
the other terms. Hence the canon of this Figure will be: What ARE; 
relation of deterinining (predicate) is held by either of two notions to 
a third, with which one at least is positively related ; that relation do 
they hold indifferently to each other. 

10. The syllogistic variation of Mood was seen to be evolved from 
the supreme canon of Figured Syllogism. The true number of moods 
is also to be determined by that canon. For the variety of mood 
depends on the various relations of subject and predicate produced by 
difference of quantity and quality. Hence the number of moods is to 
be determined by the number of variations in quantity and quality 
possible in the premises; and the number of valid moods, by the 
number of these variations in which both premises are not negative 
and in which the quantifications of the middle term, whether as on 
or predicate, exceed the quantity of the term taken in its whole ex- 
tent (i.e. where the middle term is distributed). When some others 
are excluded which have particular conclusions where universal are 
competent, there remain in all thirty-six valid Moods, twelve affirmative 
and twelve negative. These Moods are all evolved from the supreme 
canon of Figured Syllogism, and are independent on the variation of 
the various Figures. Hence they are valid in every Figure. Each one 
of them may be evolved from the supreme canon without reference to 
the others, and therefore they are mutually independent. The variation 
of moods in the different Figures under the Old Analytic was caused by 
the confusion created by not quantifying the predicate. When that 
confusion is cleared up the moods are seen to be virtually identical or 
relatively equivalent throughout every variety of schematic difference. 

11. In the Second and Third Figures, where the extremes both 
hold the same relation to the middle term, there is not, as in the first, 
an opposition and subordination between a term major and a term minor, 
mutually containing and contained, in the counter wholes of Extension 
and Comprehension. In the First Figure, since the major term is pre- 


! Hamilton’s Lect. on Log. p. 350; ef. Discussions, pp. 654, 655. 


Sir W. Hamilton's Logical Notation. 567 





licate of the one premise and the minor term subject of the other, in 
the whole of Extension the major is greater than the middle, and there- 
fore much greater than the minor term; while in the whole of Com- 
rehension the minor is greater than the middle, and therefore much 
sreater than the major term. But in the Second Figure both major 
and minor terms are subjects in the premises, and in the Third Figure 
they are both predicates in the premises; and the mutual subordina- 
tion cannot arise. Consequently, in the Second and Third Figures 
there is no determinate major and minor premise, and there are two 
indifferent conclusions. For example, we may equally well say— 


Second Figure Third Figure 

PMorSM MP orMS 
SM PM MS MP 
SP PS SP PS 


Whereas in the First Figure the premises are determinate, and there 
is a single direct conclusion. For example, we must say— 

MP 

SM 

SP: 
and since every proposition is an equation, we may have also the ın- 


direct conclusion P 8. 

12. In the First Figure, Comprehension and Extension are in 
equilibrium, the major and minor terms are reciprocally whole and 
part, and this Figure is, therefore, common to Induction and Deduction, 
indifferently. 

In the Second Figure, Extension is predominant, for the predicate is 
naturally the greater, and this Figure is, therefore, more appropriate to 
Deduction, which proceeds from the universal to the particular, from 
what is true of a class to what is true of individuals. 

In the Third Figure, Comprehension is predominant, for the subject 
is naturally the greater, and this Figure is, therefore, more appropriate 
to Induction, which proceeds from the particular to the universal—from 
what is true of the individuals which make up a class to what is true 
of the class itself. 

$ 9. III. The scheme of logical notation is meant to show, with 
mechanical simplicity, all the propositional and syllogistic forms. Sir 
W. Hamilton! intends this scheme to be wholly different in principle 
and perfection from those which have been previously proposed, but, as 
Archbishop Thomson says, ‘many of the different elements are not new.’ 

This notation ‘can represent any relation of the terms, any order of 


1 Lect. on Logic, ii. 251. 








en 





Se a> ae τον ἄν 





= Ss τ -- = ~~ I — en 3 > bi 
2 Bun 5 ms ‘ aa “ - : a ai nn 
——— ee Sa αο- -"- eee ve wren ee arse eee - 


568 Appendix A. 





the proposition, any extent of quantity. The terms are represented by 
letters—the extremes by the letters C and I’, which are each the third 
letter in its respective alphabet, and the middle term of the syllogism by 
the letter M—, their quantity by the points, and the propositions by the 
lines with the letters’! ‘Definite quantity (all, any) is indicated by 
the sign (:); indefinite quantity (some), by the sign (, or ὁ). The 
horizontal tapering line (ee) indicates an affirmative relation be- 
tween the subject and predicate of the proposition. Negative is marked 
by a perpendicular line crossing the horizontal (ye). . . . In Ex- 
tension, the broad end of the line denotes the subject, the pointed end the 
predicate. In Comprehension this is reversed; the pointed end indi- 
cating the subject, the broad end the predicate. . . . A line beneath the 


three terms 
( C—i \ — T 
> 


denotes the relation of the extremes of the conclusion. . . . In the 
Second and Third Figures,—a line is inserted above as well as below 
the terms of the syllogism, to express the double conclusion in those 
figures. The symbol (~—) shows that when the premises are con- 
verted, the syllogism remains in the same mood; the symbol ( x 
shows that the two moods between which it stands are controvertible 
into each other by conversion of their premises.’ ? 
The mood Barbara is thus expressed by Hamilton’s notation :— 


C, — u : M, -ιὐἀδ᾽ I; 

EEE 
and the mood Celarent thus :— 

C: ——__a: M, —,: I. 


ἜΤ --. --- 


This New Analytic is almost entirely based upon the doctrine of the 
Quantification of the Predicate, and stands or falls with that doctrine. 
For a criticism of the doctrine, cf. Appendix B, p. 579. 

Archbishop Thomson, who does not accept all the results given 
above, gives the most complete exposition and application of the 
doctrines in his Outlines of the Laws of Thought. 

§ 10. The doctrines contained in this New Analytic of logical 
forms lead directly to the theories of Boole and Jevons. 


Boole's Logical Theories. 








RN BSS 
to assimilate all propositions to the type of mathematical identities, the 
copula being reduced to a mere sign of identity between ae extension 
of the subject and the quantified Predicate. In Boole’s Laws of 
Thought, the analogy thus suggested between the processes of formal 
Logic and the methods of Arithmetic is worked out into a complete 
theory of symbolical reasoning developed from fundamental laws, in 
great part precisely similar to the laws of Operation in Mathematics. 
That is, the premises of an argument expressing given relations among 
certain logical elements, Boole undertakes by symbolic methods to 
climinate those elements which we desire not to appear in the 
conclusion, and to determine the whole amount of relation implied by 
the premises among the elements which we wish to appear, and that in 
any proposed form. To this end he divides Propositions into Primary 
Propositions expressing relations between things (Categorical), and 
Secondary, expressing relations between Propositions (Hypothetical). 
His method is originally developed with regard to the former class of 
Propositions, and then is shown to admit of extension to the latter also. 
A symbolical expression of the reasoning processes, of which language 
is the instrument, will embrace signs of three kinds. (1) Literal 
signs, as x, y, &c., representing things as subjects of concention—descrip- 
tive signs. [These are really signs of classes, the symbolical method 
necessarily proceeding in extension.] (2) Signs, as +, με X; standing 
for the mental operations by which conceptions are combined. (3) The 
sign of identity =. 

The sign + adds classes, Thus, if x means men and y women, 
xy means men and women. Similarly, if z means Asiatics, x—z 
means men not Asiatics. Again, x x z means all Asiatics who are men, 
or all men who are Asiatics. It is thus indifferent whether we write 
vz or za, that is, the commutative law holds in logical as in ma- 
thematical symbolism. Again, z(c+y)=2y+22=zr+2y; 1.6.7) men 
and women who are Asiatics, or Asiatic men and Asiatic women, or 
Asiatic women and Asiatic men, are all identical conceptions. That is, 
the distributive law of mathematical operation holds here also. Further, 
the ordinary rule of transposition, by which we may write indifferently 
a+b=c or a=c—b, and the rule by which if a=, ca=cb, plainly 
hold here. There is one limitation only to our right to manipulate 
logical and mathematical identities by the same rules. From the 
identity ca=cb, which asserts that the a’s which are also c’s, and the 


gen Oo ee = Ze 
(δ. =. ee * = Ὁ my : 
-- «αἰ. -- -- .- ~~ =: 2 ie 
ee ᾿ » = 


A leading characteristic of the Doctrine of the Quantification of the b’s which are also c’s, are identical, we cannot infer that all a’s are b’s 
Predicate, and other [recent | theories of a similar kind, is the attempt (a=b). 


Connected with this peculiarity of logical symbolism is the 
Η ΄ ΄ 4 ’ 
following remarkable law : xa or x? means all x’s that are 2’s, and so 


Sn. 


= 


— 


1 Baynes’ New Analytic, p. 151. 2 Hamilton’s Lect. on Log. ii. 473. 


τ΄... .“-.- ---- 4-ώ-...5 


nn -ος- 
uud Luc ας Firm dr 


sus 








570 Appendix A. 





is simply =z. This result 2?=x is, in fact, the keystone of Boole’ 
method when put in the shape z(1—x)=0. But to understand τὰ 
result in this shape we must have a meaning for 1. In rn 
1 satisfies the equation 1 x y=y, whatever y is. This will be true ie 
Logic also, if 1 represents a class which contains all y’s, whatever » Ἢ 
that is, if it be the Universe [of logical extension]. This being <a 
see at once that 1— x means all not —x’s, and the equation x(1 ace 
means that no 2 can also be a not —2, the law of Contradiction This 
very remarkable deduction of the law of Contradiction is ie the 
only one of Boole’s results which can be fully stated without an amor ; 
of symbolical apparatus which would be out of place here But it 
will be seen that the symbols and methods just described ‘th th 
addition of an indefinite v to mark particular terms [e.g. if x fie 
men, ve means some men] suffice to express any proposition ia 
identity. The symbolically expressed identity may then be mani 
lated like an equation, save only that we must not divide out a es 
factor. The equation may take a shape not logically interpretable; but 
a purely symbolical rule, corresponding to Taylor’s theorem in al she 
suflices to reduce any expression, however complex, to a en 
which can at once be read back into ordinary language, and ἴω 
exhaustively all the relations logically implied between the a of 
the original proposition. If the premises form more than one proposi- 
tion, the whole system can be reduced to a single final Er 
the interpretation of which in like manner exhausts the logical dolitions 
implied in the premises. But usually, as in syllogism, it is δύω to 
eliminate one or more middle terms from the sonidhunion, and here, too 
Boole’s method is general, providing, by an application of the dene 
mental principle 2(1—zx)=0, for the elimination of any number of 
terms from any proposition or system of propositions. Of this general 
method the laws of syllogism are merely special cases, and ie hi 
as Boole urges, do not appear to be fundamental. On the contrary, | | 
concludes that all reasoning -does not consist of elimination an 
syllogism is not the natural type of elimination, and τὰ that the 
Aristotelian or scholastic logic is not a science but a collecti f 
scientific truths, incomplete and not fundamental. i 
Proceeding to discuss the Logic of Secondary Propositions, Boole 
argues thus:—The secondary proposition, ‘If X is, Υ is,’ siden that 
the proposition X is true at the time when YF is true, wales that other 
secondary propositions may be explained with reference to time Now 
let x, y denote the times during which X, Y are true. Then = ae 
y+ will mean the aggregate of these tines, xy or yx will be the ie 
during which both X and Y are true. Thus the commutative nd 


Prof. Fevons' Logical Theorves. 571 








distributive laws hold here also. In short, the laws of operation for 
x, ἡ, &Cy Which now denote parts of time, are just the same as the 
laws already developed for symbols denoting parts of the universe. 
For example, #(1—«)=0 has the meaning that the proposition X 
cannot be both true and false at the same time, and from this starting 
point the whole Logic of Secondary Propositions flows on in the exact 
shape taken by the Logic of Primary Propositions. The importance 
which ‘ pure time’ thus acquires in symbolical logic, as in the more 
speculative part of modern algebra, is very striking, and Boole remarks 
that the theory of Primary propositions might similarly have been 
founded on the Conception of space." But that such a use of the 
notion of space is not necessary seems to him to be in harmony with 
the fact that a geometry of space of more than three dimensions is 
analytically possible ; and suggests the observation that there seem to 
be grounds for thinking that the manifestation of space to the human 
mind, but not that of time, might have been otherwise than it is. 
[Boole’s work contains also a theory of probability, which need not be 
discussed here, and closes with a striking metaphysical chapter on the 
nature of science and the constitution of the intellect. | 

§ 11. Professor W. Stanley Jevons,? like other logicians who base 
their systems on the quantification of the predicate, starts with the 
doctrine that the proposition is an equation of subject and predicate. 
He objects to Dr. Boole’s method, because it ‘shrouds the simplest 
logical processes in the mysterious operations of a mathematical cal- 
culus,’> forgetting that it was Dr. Boole’s express design to show that 
Logic was really a department of mathematics, and its operations ‘to be 
followed only by highly accomplished mathematical minds.’ For this 
and other reasons Professor Jevons thinks that the ‘true clue to the 
analogy of Logic and mathematics has yet to be seized,’ and that he 
himself has discovered it. He shows that when a proposition is re- 
garded as the equation of two terms, the terms need no longer be distin- 
guished as subject and predicate, but become convertible, and for the 
copula may be substituted the sign of equality (=). When the equa- 
tion is thus taken as the fundamental form of inference, and the dis- 
tinction of subject and predicate abolished, the fundamental formula for 
reasoning will be: whatever is true of a thing is true of tts like, and the 
fundamental principle of reasoning is the SUBSTITUTION OF SIMILARS. 


1 Is there not a confusion here similar to that which led Hamilton (and with 
him Boole also) to represent Kant’s forms of intuition as forms of thought ? 

2 The Substitution of Similars the True Principle of Reasoning. London, 1869. 

3 Phil, Trans. of the Royal Society of London, vol. elx. pt. ii, 449. 





572 Appendix A. 


δεν «ΩΣ LS 
: Aa power always resides in equality. Difference as such cannot 
. = . 
allord any inference. For example, if we have 
a=b a 
|| we may infer by substituti 
Ι y N , by substituting c for b; but if we have 
a~b 


? 


He shows how the ordinary syllogistic moods may be obtained, si 
and directly by means of his fundamental principle, and on ed 
forms of immediate inference rest upon it; but has ie worked : εἰ, 
theory ei all its details. The great novelty, however, in cies 
Jevons view of Logic is, that just as Dr. Boole BE Logi =: 
mathematical calculus, so he brings it to certain mechanical οἷα μι 
which can be exemplified, or rather performed by a il niin 
This logical analytical engine is described in the ‘Phil ie τὸ μὰ 
een Society of London,’ vol. 160, pt. ii. p. 497: On the a 
ee er Logical Inference. To such lengths has Formal Logie 
As Professor Jevons’ logical theories depend upon the doctrine of 
the quantification of the predicate, and stand or fall with that do tr 
they do not require to be here discussed. It would not ie 4 | 
right to pass from their consideration without noticing that the ita ‘ 
of substitution of similars, as the true principle'in BEER which Pro- 
fessor Jevons claims to have discovered and placed in its vightful idles 
as the fundamental principle of deductive: inference att we ἴων 
enounced to be so by Dr. Fr. Ed. Beneke, was ἀἰισαυνοῦ b Ἴων pr 
say nothing of others) in his logical writings, and is so weil TR 
and recognised in Germany as a logical principle, that t | a 
devote a paragraph to its discussion.! sate 
§ 12. The logical system which has been elaborated by Mr. J. S 
Mill? is very far removed from the systems of Formal Lo M ER , ed 
above. Mr. Mill belongs to that school of Philosoph “which ad 
nental critics are dispesed to regard as the typical English He ie 
inheritor of the ideas of Hobbes, Locke, and Hume. t ie and : a 
especially the Syllogistic, has never been a favourite ‘aid witl u 
thinkers, and has even been expressly neglected by ei = th 5 
Mr. Mill has done this service for his fillow-Giinkers : ci t τὰ 
what they believe to be the dry bones of a dead Scheitelleien 5 δ 
quickened them into life, making them fit for service id nr ie 


1 Cf. above, § 12 
above, § 120. * System of Logic, 7th ed., 1869. 


Mr. Mili’s Logical Theories. 73 











inspiring them with the spirit of his sensational philosophy. He has 
seen the value of a system of Logic to be the iron edge to the wedge 
of sensationalist metaphysics. Hence it is, that with Mr. Mill, more 
than with any other logical writer, logical theories are almost entirely 
dependent on a’particular metaphysical solution of problems of know- 


ledge, and logical criticism becomes a defence and attack of metaphy- 


sical theories. 
Mr. -Mill’s problem seems to be: Given sensation and a multiplex 


association as the sole matter and form of knowledge, to construct a 
theory of evidence which shall fitly appropriate all the old scholastic 
logical nomenclature, and be for us, with our present opinions, a real 
Logic. And the task is accomplished with such freshness of insight, 
that we must admire.the ability of the thinker, however much we 
dissent from the fundamental doctrines on which he builds his theories. 

Mr. Mill’s logical doctrines cannot be understood nor appreciated 
apart from the remembrance of the fact, that he believes knowledge to 
be the joint result of sensation and processes of association. This fact 
lies at the basis of his logical opinions, and everywhere modifies them. 


Things are congeries of sensations to which we ascribe a unity, because 
Judgments are statements of the co- 


they are inseparably associated. 
Inference is proceeding from one 


existence of two sets of attributes. 
to another set of associated phenomena. 

According to Mr. Mill, Logic is the science of the operations of the ı 
understanding which are subservient to the estimation of evidence ; 
both the process itself and all other intellectual operations, in so far as , 
It attempts a correct analysis of the intel- 
and of such other mental 


then on the foundation of 


they are auxiliary to this. 
lectual process called Reasoning or Inference, 
operations as are intended to facilitate this ; 


this analysis, it brings together a set of rules for testing the sufficiency 


of any evidence given to prove any proposition. 
from this definition, a theory of Logic falls naturally into 


Starting 
heory of proposition, and a 


three divisions—a theory of naming, a t 
theory of inference. 

§ 13. A Name is defined to be ‘a word or set of words serving the 
ark to recall to ourselves the likeness of a former 
Names which stand 
e individual 


double purpose of a m 
thought, and a sign to make it known to others.’ 
for individual conceptions, and correspond to the objectiv 
existences, are not distinguished from names which stand for general 
rrespond in their content to the essence, 


conceptions or notions, and co 
1 The categories of Aris- 


and in their extent to the genus or species. 


1 Cf. above, § 8, p. 17. 








574 Appendix A. 





totle are considered to be a haphazard classification of Nameable things, 
and are superseded by one which is considered simpler and better 
fitted to represent the real nature of the case.! The Predicables are also 
retained but transformed. The objective fact on which this five-fold 
classification of predicates is made to rest is the real existence of kinds, 
Every class which is a real kind, i.e. which is distinguished from every 
other class by an innumerable number of attributes, may be a genus 
or a species. Starting from this fact, the five predicables are easily 
evolved. A Genus is a kind which includes other kinds. A Species is 
a kind which does not include other kinds. If it be looked on ἃς ἃ 
kind with reference to other kinds above it, it is a Species predicabilis ; 
if looked on as a kind with reference to individuals below it, it is 
a species subjicibilis. The other three predicables are founded on the 
connotation of the name of the species. The Differentia is that part of 
the connotation of the specific name, ordinary, special, or technical, 
which distinguishes the Species from all other species of the Genus to 
which we are for the time being referring it. The Property is an 
attribute belonging to all individuals of the Species, which, though not 
ordinarily annoted by the specific name, follows from some attribute so 
annoted, either by demonstration or causation. An Accident is any 
attribute belonging to the Species, which is neither involved in the 
name nor follows from any attribute so involved. If it belongs 
universally to the Species it is inseparable ; if it does not, it is separable. 

The great defect in Mr. Mill’s theory of names is, that while he 
distinguishes simply and clearly between the extent and content of 
notions in his remarks on the denotation and annotation of names, he 
has not referred these distinctions to their objective realities on which 
they depend, and to which they conform. The extent of the notion 
depends on the real existence of the species or kind. This Mr. Mill 
acknowledges, but does not apply. The content of the notion depends 
on the real existence of the essence. This Mr. Mill denies. He ac- 
knowledges no essence but the nominal, which itself depends on the 
content. 

$ 14. In his theory of Predication, Mr. Mill begins by laying down 
a fundamental principle, the truth of which cannot be too often 
asserted—propositions are assertions about things, and what is οἱ 
primary importance to the logician in a proposition is the relation 
between the two phenomena to which the subject and predicate respec- 
tively correspond. He then shows that other theories of predication, 
and especially the theory of the upholders of Formal Logic, have 


1 Logie, i. $ 15. 


Mr. Mill’s Theory of Predication. 575 








neglected this fact, and in neglecting it have been led to dwell exclu- 
sively on the denotation of the subject and —— and τι > 
proposition the statement of a relation between two classes : " jee ὦ 
A theory of predication must make prominent the connotation Οἱ the terms 
used, else it will not express that reference to fact which predication 
‘nvolves. In this way Mr. Mill evolves his attributive theory of predi- 
cation—which asserts that the true import of the proposition ‘ All men 
are mortal’ is: Whatever has the attributes of man has the attribute 
of mortality, or: Mortality constantly accompanies the attributes of 
man. One class of propositions, however, do not assert matters of fact. 
They only declare the meaning of names. These propositions may be 
called verbal, while others are real. A verbal proposition conveys no 
information to any one who previously understands the full meaning of 
the term, and when any important consequences seem to follow from 
such a proposition (as they do in mathematics), these consequences 
really flow from the tacit assumption of the real ewistence of the object 
so named. The most important class of verbal propositions are Defini- 
tions. No Definition is meant to explain and unfold the nature of a 
thing; it is simply a proposition declaratory of the meaning of aterm. 
It is always nominal. What are called real definitions are merely 
nominal definitions with an ippligd postulate that the object denoted 
by the name exists. Mr. Mill’s ,attribuave theory of the syllogism is 
based on this theory of Predication and cn his explanation of the nature 
of Demonstrative truth. u. 
When Mr. Mill says that propositions are assertions about things, 
he does not go deep enough. A proposition is the expression of a 
relation in thought which corresponds to and mirrors a real relation in 
things. This real relation is not mere co-existence, it is generally Ὁ 
subsistence and inherence. What is represented by the subject is seen 
to be something which subsists, and what is represented by the predi- 
cate is seen to be something which inheres in what subsists. Mr. Mill’s 
fundamental error of refusing to admit the real existence of the essence 
as he does the real existence of the species prevents him from follow- 
ing out the true theory of predication. The acknowledgment of Ἧ 
real essence would give a unity to the subject which in Mr. Mill’s 
theory it does not possess, and make it something different from the set 
of attributes more or less indefinite, which Mr. Mill makes ıt to be. 
This error comes out more especially in the theory of Definition. 
Definition is not merely the declaration of the meaning of a word—1.e. 
the statement of the connotation. It is the expression of the Essence. 
Now Mr. Mill recognises no Essence save the nominal essence, which is 


merely the approximately correct connotation. 





ote 


ee A ee ante ein nn 
= = oa 5 z z Pr 


sr 





ee 











576 Appendix A. 





§ 15. Inference or reasoning in the most general sense results when 
a proposition is believed as a conclusion from something else. The 
so-called immediate Inferences of logicians are not inferences properly 
speaking, because no new truth is arrived at in the conclusion. Infer- 
ence only occurs when we proceed from the known to the unknown. 
Inference in this sense is of three kinds: reasoning from generals to 
particulars— Ratiocination or Syllogism ; reasoning from particulars to 
generals—Induction ; and reasoning from particulars to particulars—a 
kind not often noted, but the basis of the other two. 

Syllogism is usually thought to be the universal type of all reason- 
ing. So far from this being the case, the truth really is that if we take 
syllogism to be a process of inference at all, we cannot avoid the con- 
clusion that it is a Petitio Principii. If we are to get out of the difü- 
culty, we must distinguish the process of inference from the process of 
registering the results of inference. The usual theory of the syllogism 
ascribes to the latter the functions of the former. All true inference is 
the associative inference irom particulars to particulars. We store up 
the results of such inferences in general propositions, and in this way 
they become registers of a multitude of past inferences, and short 
formule for making more. The majox premise of a syllogism is such 
a register and formula. The conclusion is not an inference drawn 
from the formula, but according to:it. In the syllogism we do not 
infer, we only decipher our noses. " I:he‘true logical premise is the par- 
ticular facts from which the genera] premise was gathered. Hence the 
dictum of Aristotle does not give a true type nor correct formula for 
the syllogistic process. Every reasoning may rather be reduced to this 
form : 

Certain individuals have a given attribute ; 
An individual or individuals resemble the former in certain 
other attributes. 
.*. They resemble them in the given attribute also. 


In this way the legitimacy of every inference is to be decided by the 
canons of induction; and general propositions are retained as useful 


registers and abbreviations in reasoning. 

The strongest objections to this theory of the Syllogism may be drawn 
from the Demonstrative Sciences. They are supposed to have a pecu- 
liar certainty of their own, which rests in the force to prove lying in 
the major premise. Against such objections Mr. Mill brings his theory 
of Demonstrative Science; which is based on his theory of Definition. 
The peculiar certainty and accuracy of Demonstrative (e.g. geome- 
trical) science is fictitious and hypothetical. For every Demonstrative 
Science depends on Definitions and axioms. Now the axioms of 


Mr. Mill’s T heory of Demonstrative Science. 577 





Geometry are merely generalisations from experience—an experience 
which constantly recurs, is never broken by contradictory cases nor 
even by contradictory analogies, and so is very strong. ‘The Definitions, 
again, do not admit of consequences concerning the nature of things, 
because they are only declarations of the meanings of words. The 
consequences deduced follow from the assumption that there is a real 
thing exactly conformable to the definition. This assumption is only 
approximately true in Geometry. There are no actual circles exactly 
correspondent to the definition of a circle, &c. And the conclusions in 
Geometry are true only in the ratio of the approximate truth of the as- 
sumption. The peculiar accuracy in Geometry is therefore hypothetical, 
and any number of sciences might be constructed, having the certainty 
of Geometry, by combining a set of definitions with a few real axioms. 

Mr. Mill’s theory of Definition, on which this somewhat strange con- 
clusion regarding the nature of mathematical certainty rests, has been 
already noticed; but even if his theory of Definition were correct, 
objections might be taken to the conclusions he founds upon it. 
Mathematical notions become fruitful and produce mathematical 
science, not by being verbally defined, but by being actually realised 
as primitive elements of intuition ;—not as merely subjective elements, 
but as real elements in rerum natura, which the mathematician seeks 
to apprehend in their primitive generality and simplicity, and to carry 
out into their real (not formal) consequences.’ And no branch of know- 
ledge wherein the notions it contains cannot be apprehended in their 
primitive generality and simplicity in intuition, can reach the certainty 
of Geometry. Wolff’s science of Architecture was formed after the 
plan described by Mr. Mill, but it does not possess mathematical 
certainty. 

§ 16. Mr. Mill’s labours in founding a systematic theory of Induction 
cannot be altogether passed over. His primitive type of reasoning is 
the associative impulse; and when this has created for itself a basis 
(the law of Causation) on which it may rest while advancing beyond 
particulars to generals, and has formed certain rules or canons by which 
it may so vary its processes as to exclude, more or less thoroughly, the 
entrance of error (the Inductive Methods), it becomes Induction. Mr. 
Mill differs from his predecessor in the same department of logical 
enquiry, Dr. Whewell, in the view he takes of the general character of 
Induction. He complains that Dr. Whewell does not distinguish be- 
tween Colligation of facts—i.e. the collection of instances and their union 


' Cf. two Papers read before the Royal Society of Edinburgh, by Prof. W. R. 
Smith, ‘On Mr. Mill’s Theory of Geometrical Reasoning,’ and ‘Hegel and the 
Metaphysics of the Fluxional Calculus.’— Transactions, vol. xxv. 

= 











578 Dr. Whewell on Induction. 





under a mental conception which binds them together—and Induction 
proper. The former is mere description. It does not proceed to the 
unknown. Induction goes beyond the facts either to their explanation 
(i.e. the determination of the conditions under which they now occur), 
or to their prediction (i.e. the determination of the conditions under 
which similar facts may be expected again to occur). Kepler's theory 
of the elliptical orbit of the planets was a mere description or Colliga- 
tion of Facts. Newton’s doctrine that the planets are moved by the 
composition of a centripetal with an original projectile force is an 
Explanation or Induction. 

Dr. Whewell, on the other hand, declares that Mr. Mill, by asserting 
that the Colligation of Facts is not Induction and that it does not introduce 
a new element of knowledge, misses one of the.most important things in 
all inductive enquiry—the true meaning and power of the mental 
conception which binds the facts together. To separate the explanation 
of facts from their colligation, and to introduce elaborate methods for 
attaining to this explanation, is to degrade the theory of induction and 
the philosophy of discovery to a mechanical method, and to neglect too 
much the peculiar power of the mind to frame scientific ‘ ideas,’ apply 
modified conceptions of these to the particular instances, and so explain 
the facts. Dr. Whewell would do away with Mr. Mill’s inductive 
methods altogether, and give instead rules for framing suitable con- 
ceptions. 


T. M. L. 














APPENDIX B. 


THE DOCTRINE OF THE QUANTIFICATION OF THE 
PREDICATE. 


The doctrine of the Quantification of the Predicate has held such an 
important place in all recent English logical speculation, that it deserves 


to be specially discussed. . 
The Quantification of the Predicate was discovered and applied with 


more or less fulness almost simultaneously by Dean Mansel, Arch- 
bishop Thomson, and Professor Sir W. Hamilton. But as Sir W. 
Hamilton has stated, developed, and applied the doctrine in a much 
fuller and more systematic way than any other, we shall only notice his 


exposition.! 


ı For a statement and discussion of the various partial antieipations of the 
doctrine of the quantification of the predicate, compare Sir W. Hamilton's Lect. on 
Logie, vol. ii. 298 ff. ; and Prof. Thomas S. Baynes’ New Analytic of the Forms 
of Thought, p. 81 ff. A word may be added on the claims of two modern writers 
on Logie, to the discovery of the doctrine, unnoticed in either of these statements. 
Prof. Beneke, of Berlin (ef. above, p. 219), enounced that substitution was the 
principle of all analytical syllogisms. We advance from the known to the unknown 
by substituting one notion or one term for another. He saw that this principle 
implied that what is substituted must be equal or of less extent than that for 
which it is substituted, and that as predicates are among the terms substituted, 
their extent must be definitely known. This clearly implied the quantification of 
the predicate. But Beneke stopped short before enouncing it, and his new 
analysis of Logic, which really rests on the doctrine, is thus one-sided, confused, 
and unsystematic. He saw, rightly we believe, that the predicate is really and 
naturally attributive, not quantitative nor expressive of extent, and would not 
therefore quantify it in any thorough-going way. He did not see that his doc- 
trine of Substitution involved the quantification of the predicate, and therefore did 
not abandon the former when he rejected the latter. (Cf, Syll. Anal. Orig., &c., 
Berol., 1839.) ! : 

George Bentham (A New System of Logic, &e., Lond., 1827), is said — τα 
have anticipated Hamilton in enouncing and applying to Logic the doctrine of ἃ 
quantified predicate. The assertion cannot be justified. He did enounce the fact, 


PP 2 

















580 Appendix B. 





The doctrine of the Quantification of the predicate demands that 
the quantity of the predicate be explicitly stated. According to the 
common logical rules in force since the days of Aristotle, the predicate 
is not regarded as possessing any quantity of its own. When there is 
occasion for marking its quantity, as in conversion, a borrowed quantity 
dependent on the quality of the proposition is attributed to it. All 
affirmative propositions are said to have predicates whose quantity is 
particular, e.g. All men are mortal when converted becomes Some 
mortal beings are men, not all mortal beings are men. On the other 
hand, the quantity of predicates in negative propositions is universal, 
e.g. No merely formal Logic is a true theory of knowledge when con- 
verted becomes No true theory of knowledge is a merely formal Logic, 
not Some true theories of knowledge are not.a merely formal Logi. 
The doctrine of the quantification of the predicate would make the 
quantity of the predicate as self-dependent as that of the subject is, 
and would give to the predicate the same quantitative predesignations 
which are attached to the subject. The immediate effect of this doc- 
trine is to double the number of the propositional forms. For quantity 
is either universal or particular, and each of the four common forms of 
propositions takes a double form as its predicate is universal or parti- 
cular. Thus— 


(I.) A. All S are P, becomes ee S are all P 


All S are some P 


Some S are all P 
Some S are some P 


; are 


(11.) I. Some S are P, becomes | 


Any S are not P 
II.) E. NoS P ς Υ ot any 
(HL) o § are P, becomes ων S are not some P . ENO.* 


(IV.) O. Some § are not P, Fe S are not any P . ONE. 


becomes . Some S are not some P . ONO.* 


This doctrine of the Quantification of the Predicate is based on the 
fundamental postulate of Logic: State explicitly what is thought im- 


but not with such fulness of meaning and application as was afterwards done. 
His chief service lay in this, that he was one of the first to clearly conceive and 
assert that a proposition was only an equation of the subject and predicate. 

1 The forms marked with an asterisk are the new ones. Fand N are used to 
denote affirmative and negative moods, being the first consonants in the verbs 
affirmo and nego. Since the subject must be equal to the predicate, vagueness in 
the predesignations must be as far as possible removed. Some is taken as equi- 
valent to some but not all, and in negative propositions all is discarded for any. 
All men are not black might mean some men are black. It should be noticed that 
Archbishop Thomson does not adopt all the new forms, but only the affirmative 
ones (1 and 3). 


The Quantification of the Predicate. 581 











plieity. | This postulate has only to be stated to be accepted, and 
whenever it is accepted, Hamilton thinks, the recognition and accept- 
ance of the quantification of the predicate must follow. This implies, 
of course, that the predicate is implicitly thought to be a quantity, or 
its explicit quantification would not follow from the postulate of Logic. 
Unfortunately, the advocates of the doctrine have taken this funda- 
mental conception of the nature of a predicate for granted, and never 
attempted to prove that the nature of predication presupposes that the 
natural and true conception of a predicate involves the thought of 
quantity. All their arguments for their favourite doctrine are founded 


upon this assumption, and so avoid the real question at issue. Thus 
Hamilton argues :— 


1. It may easily be shown that the predicate is as extensive as the 
subject. We are conscious that the proposition—All animal is man 
or All animals are men is absurd, though we make the notion man or 
men as wide as possible ; for it does not mend the matter to say—All 
animal is all man. We feel it to be equally absurd, as if we said, All 
man is all animal. Here we are aware that the subject and predicate 
cannot be made co-extensive. If we are to get rid of the absurdity, 
we must make the notions co-extensive by restricting the wider. If 
we say—Man is animal, we think, though we do not overtly enounce 
it, All man is animal. And we think—not all but some animal. 

2. Ordinary language quantifies the predicate so often as this deter- 
mination becomes of the smallest import. This is done directly or 
indirectly. 

a. We say for example—Mercury, Venus, $c. are all the planets. 
Here the quantification is direct. 

b. We say—Of animals man alone is rational; which means 
Man-is-all rational animal. Here the quantification is indirect 
and limitative. 

c. We say—On earth there is nothing great but man; which 
means Man-is-all earthly great. Here the quantification is 


indirect and exceptive. 


3. Logicians confess that the predicate is quantified by particularity 
in affirmative, by universality in negative, propositions. Why the 


formal quantification should be thus restricted in thought, they furnish 


us with no valid reason.! 


Other arguments are added, showing that the quantification of the 
predicate is not only scientifically correct, but of actual practical value 


1 Hamilton, Lect. on Log., ii. 259. 








582 Appendix 8. 





in simplifying and completing a system of Logic. Thus it has been 
said : 

4. The progress of science demands at least the new affirmative 
forms (Thomson and Mansel). 

5. Even the new negative forms are required in logical division 
(Hamilton). 

6. The doctrine removes from Logic many cumbrous constructions 
and meaningless rules. 


These arguments, as has been said, are all repetitions with variations 
of the original assertion, that the predicate is implicitly thought as 
quantified, and that this thought should be expressed. Now we do not 
admit this assumption, and therefore do not feel persuaded by the 
arguments which it supports. The quantification of the predicate has 
been urged from the essential nature of the notion as a quantity; but 
there is a wide difference between a notion taken simply by itself, and 
a notion taken as the subject or as the predicate of a proposition. A 
notion considered simply by itself is both quantitative and qualitative. 
It denotes objects and connotes attributes. A subject notion, however, 
is naturally quantitative—denoting objects; while a predicate notion 
is naturally qualitative—connoting attributes. For a proposition in its 
simple and most natural meaning asserts that an attribute or quality (the 
predicate) is or is not possessed by a given object or class of objects (the 
subject). The inherence of an attribute in a given subsisting object is 
the natural assertion made by the simple categorical proposition. The 
relation between subject and predicate is the natural correlative of the 
real relation which subsists between a substance and its qualities. 
Hence the predicate does not naturally denote a class of objects. It's 
not naturally quantitative. We do not naturally think it as quantified. 
We think of it as expressive of a quality, and of a quality only.! 

This primary meaning of predication may be elaborated, however, 
into two secondary meanings. For— 

(1). Although the subject is naturally quantitative, denoting an 
object or part or whole of a class of objects, yet as the object possesses 
attributes, and objects are arranged in classes, as they do or do not 
possess certain attributes, the subject notion originally quantitative 
may be looked on as qualitative. The proposition will then denote 
the relation of co-existence between two sets of qualities. The set of 
qualities (which are implied by the subject) are always or sometimes 
accompanied by the set of qualities (implied by the predicate). This is 
Mr. Mill’s attributive theory of predication. 


1 Of. above, § 68, and Beneke, Syllogismorum Analyticorum Origines, &e., § 4. 


The Quantification of the Predicate. 583 

















— 


(2). Although the predicate is naturally qualitative, connoting & 
quality or qualities, yet as the presence of a quality or qualities may 
serve to denote the objects belonging to a particular class, the predicate 
notion originally qualitative may come to be looked on as quantitative. 
The proposition will then denote the relation between two classes of 
obiects; and predication may be said to be the afürmation or negation 
that one class comes under another class. This is Sir W. Hamilton’s 
theory of predication, and since it looks on the predicate as & quantity, 
naturally leads to the quantification of the predicate, and comes to 
regard every proposition as an equation of subject and predicate. 

So far, however, from this being the primary meaning of predication, 
it is only a secondary and forced interpretation of the fact process, and 
one which is only applicable in certain cases, viz., when the notion of 
the predicate can itself become substantive. Whenever the sum total 
of the objects, to which the quality expressed by the predicate belongs, 
are not all of the same kind and are not a class, then the predicate 
cannot be taken substantively, and cannot be quantified. The same 


limitation belongs to conversion. 
T.M.L. 


ı Cf, p. 295. 








ἢ 
' 
Ἷ 
i 
i 
1 
ἡ ἢ 
ry 
a 


- τοῖς. σις — = 


< 


- << 





APPENDIX C. 


THE DOCTRINE OF ESSENCE. 


The paragraph in the text upon our knowledge of the essence ($ 57) 
involves a certain amount of acquaintance with German modes of 
thought and expression, and will seem obscure and scarcely intelligible 
to many English readers. The translator, therefore, thinks it aitviesbie 
to present, as far as possible, the same thoughts in such a modification 
of expression and illustration as the necessities of translation forbade in 
rendering the passage. 

(1). The essence is always to be looked upon as a reality existing in 
rerum natura. It is not a merely arbitrary nominal essence, the ΗΝ 
or less definite and correct meaning of a term. Now, the “aes thought 
of essence implies both generality and simplicity (on the union of which 
in the ultimate elements of knowing and being the possibility of science 
rests), and both these attributes are nowhere so well seen in union as 
in the Self or Ego, which is related to, and, as it were. mingles with the 
host of fleeting impressions and phenomena which change and pass 
(generality), while itself remains stable and self-dependent through all 
(simplicity). But this Self or Ego is not at first known, nor does it 
at first exist in us. Like everything else it grows, and na to matu- 
rity by growth. At first we have only vague feelings awakened by 
the relation of our activities and conditions to our present existence 
and development. What furthers this existence and development is 
felt with pleasure, what retards it with pain. These pleasures and 
pains give us vague positive and negative notions of Self. There is one 
class of feelings which more especially gives us this knowledge—the 
ethical feelings; for the one class of actions and conditions which 
more than any there reveal to us our true independent self existence, 
is the ethical. When we truly and fully realise that we are set to 
perform certain duties, cultivate certain virtues, and possess certain 


rights, we truly and fully realise our own Self—our own essential 
existence—our own essence. 


585 


The Doctrine of Essence. 


(2). When once we have attained to the knowledge of our own ex- 
istence, it iseasy by transferring the knowledge, to recognise the essences 
of other persons. And the knowledge of the essences of others, since 
++ more sharply defines our relations, duties, and rights in connection 
with theirs, makes our knowledge of our own essence clearer. The 
knowledge of each acts on the other, strengthening and more sharply 
defining it. 

(3). When once we have reached the knowledge of personal essence, 
we have only to apply it by analogy to the world of nature, in order to 
gain a knowledge of the essences of plants and animals. And as our 
own essence is most clearly realised and defined by the round of duties 
and rights which encircle us, so their essences must be known and 
defined by the ends they fulfil, and the functions they are set to 
perform. 

(4). In the same way, the essences of the inorganic objects of nature 
is determined by the end fulfilled and function performed. It is, how- 
ever, very difficult to realise them, because we know them almost 
exclusively through their outward mechanical relations, not by any 
exhibition of an inward tendency exerted towards the fulfilment of 


o 


an end. 
(5). Artificial objects have only a borrowed ind&pendence, and their 


essence is to be sought for either in their’ analogy to self-dependent 
individuals, or in their capability to fulfil the-wsé for which they were 


intended. 
T,M.L. 








APPENDIX D. 


THE PRINCIPLES OF ETHICS. 


TRANSLATED FROM THE GERMAN OF PROFESSOR UEBERWEG. 


§ 1. Ethics is the doctrine of the normative laws of human volition 
and action, which rest on the idea (i.e. on the type-notion) of the Good. 
The place which Ethics occupies in the system of Philosophy is a 
position after Psychology, on a line with Logic and Asthetics, and 
before Paedagogic and the Philosophies of Religion and of History. 

§ 2. The psychological ‘basis of Ethics consists in the distinctions of 
value in the different mental (psychic) functions. These distinctions 
reveal themselves to us ‘immediately in the feelings, which are con- 
nected with them—oh the one side in the feelings of pleasure and pain, 
and on the other in the feelings of approval and shame. The distinc- 
tion between what aids and what hinders reveals itself in pleasure and 
pain, and the distinction between higher and lower functions in the 
feelings of approval and shame. Feelings precede ethical notions and 

judgments. Their universal existence and importance is based upon 
the similarity of the human nature and exists in so far as this similarity 
exists, 

§ 3. These distinctions in value are immediately connected with the 
mental (psychic) functions themselves, and mediately with whatever 
condition these mental functions. A Good is what makes those mental 
functions possible which are revealed by feelings of pleasure or ap- 
proval. The sum total of everything Good, belgnging to the human 
race, is the ‘Highest Good’ in the collective sense (Summum Bonum). 
The relative values are connected partly with the connections which 
exist between the different classes of functions of the individual, or 
between the actions of the different faculties of the soul (for the actions 
of the higher faculties are of more value than the actions of the lower), 

partly with the ties which connect the individual with the surrounding 
community (since the requirement of a greater number of persons 1s 


Rights and Duties. 987 








of more value than the requirement of a lesser number (or = an nt 
dividual of this number.) The idea (the type-notion) o . 
self-regard starts from the first, the idea of the common weal iro 
εν py whole ethical problem for mankind is gradual ge 
tion to the realisation of the Highest Good. This ES i a 
solved by the co-operation of all persons interested. Lai our ne _ 
in order to procure any good whatever. The distribution 0 : 5 
total of labour among the different members of the community = 
more and more qualitative with the progress of development. very 
individual no longer works at the same labour in his own province 
which others work at in theirs, but each individual endeavours to m 
duce one kind of product, and exchanges with his neighbours for ot - 
The existence of the community is conditioned by a limitation = 
share of each member to his labour and the results of his labour. is 
share is determined partly by the community, by means of = age 
ment of its collective will, and partly by the individual himse = a 
sphere of free self-determination which belongs, N e ed 
minations or rules which are universally true, to the individua re N 
the lesser community within the more comprehensive en ἊΝ 
the Right of the individual or of the lesser community. The — 
of these determinations is the ‘ Right,’ in the somes oan ο > 
word, which prevails within the community. To τ — 
‘Duty,’ or the sum total of what every member of t . —_— - en 
to do or to suffer in order to fulfil the final end of the who e. : : y - 
reference to a sphere of rights to which we do not belong τ e = > 
by the will of persons authorised to do so; Duty with re wie N 
own sphere of rights is determined by our own consciousness. on 
arises the distinetion between a Duty of Right and a Duty o το 
science. The latter is the ‘moral duty’ in the stricter sense. ; 8 
limitation of spheres of Right by each other is ge by _ a 
an order of rights, and this order 1s maintained by the - er 
authority and obedience. He who bears the authority an = pest 
the power which the authority exercises over the members ο seabed 
munity is its Head. The State is the most extensive peste y oar 
one head which aims at reaching an ethical end by means of t 16 c ei 
fication of rights. The essential functions of States are: to give = 
or the determination of the classification of rights, just decision μη Ἢ 
application of this classification of rights to digpiiabte Bi er 
choice or direct appointment of individuals by means ΟἹ the εν 
choice of the State, and in an analogous way by lesser commun 
within the sphere of their right. 





588 Appendix D. 





§ 5. The application of the law to the individual cases follows by means 

of an inference, whose major premise is the law itself, whose minor is 
the subsumption of the individual under the subject notion of the law, 
and whose conclusion is the reference of the predicate notion of the 
law to the individual. The universality of the major premise of this 
syllogism may be actually denied by the lawful opinion and action of 
the members of the State; the subsumption given in the minor pre- 
mise may be debated between different persons concerned. In bot} 
cases the State exercises its 
framed for the purpose by itself—criminal justice and civil justice. 
The security of the classification of rights, as opposed to the possible 
contradictory wills of individual persons, is attained by threatening 
punishment and by means of actual punishment. It is not a correct 
view of punishment to say that its use is only preventative, and as a 
warning. The wrong which consists in transgressing upon the arrange- 
ment of rights is followed by pain which injures, and is of the same 
kind as the pain we suffer in our consciousness. This consciousness 
opposes the motives which incite us to break the laws. In the same 
way the community opposes punishment to law-breaking, and by not 
allowing it shows that it is not a participator in the licence. Punish- 
ment, limited according to law, is in comparison with direct coercion, 
the correct measure of personal freedom taking the form of the re- 
action of ordinance—the State against contradictory individual wills, 
The highest problem is to avoid, as far as possible, collision by means 
of the greatest harmony possible between the law of the community 
and the sentiments of its members. 

§ 6. Within his own sphere of rights every person has to co-operat 
in the gradual realisation of the highest good. In this consists his 
moral duty. The moral law takes the following formula: Act within 
the limits of your own sphere of duty, so as to solve the great problem 
of humanity as far as possible. This law demands, above all, that 
some work be done in each one’s vocation, i.e. in the sphere of labour 
determined by the principle of the division of labour. All other action, 
however, finds also the criterion of moral value in th 
one must strive at all times to make the most valuab 
possible contribution to attain the en 
classification of value w 
The reason determine 


1 


e demand: each 
le or the highest 
d of mankind, according to the 
hich is founded upon the essential nature of man. 
S how every single end is to be followed out 
according to its position within the totality of ends (Aristotle postulates 
this, but not very determinatel y), according to a mean between its over 
and under estimation. The egotistic tendency to overestimate our 
own ends, which tends to disturb our true estimation of their relation to 


lawful function by means of an instrument . 


Legality and Moralıty. 589 





the sum total of the problem of mankind, may = checked Py a 
| i our 
i ible or desirable that the maxim o 
whether it would be possi Sa 
ll persons, or serve fo Ρ 
should be followed out by al ΓΒΟΙ : — 
ern legislation. But this principle is not to be an ii 
ὩΣ significance in Ethics (as Kant nn = It ıs = , Fe 
᾿ i inci f allowing the fullest scope 
n the Ethical principle o = 
= of the whole task of mankind. There is a more or less certa 
: : . . 
approximation of different ends to ar " gO set 
inati individual ends desirable to 
The subordination of indivi ee 
i i total of ethical duty which fa 2 
the ethical law is the sum a Ho 
inati indivi l ends desirable by others un thic 
subordination of individua a Ὅκου 
i thical duty which falls to others. 
law is the sum total of e soe 
Satie is theoretical only, for practically every kind of duty w 
3 also. 
0 ns ourselves concerns others a | | 
Ἶ (7. Virtue is habit in accordance with the ethical problem, or the 
“a i aptitude of the will. Habit (as Aristotle has ἐν ἐπ ὁ ae 
WAN j j 1 , t tendency o 
i i 1 ts of will, and is a permanen 
arises from single similar ac a 
iti ain, the subsequent acts of will. g 
the will. It conditions, agaın, ' Er coy 
Ἷ he ethical view becomes the c ary 
full development when t teachings: κοι 
iginally confined to a single instance, pe 
The ethical view, originally nn 
i 1 hich rests on a comparison Ὁ gs by 
into an ethical consciousness w er 
formance of deeds comman y 
ns ofthought. The mere per 
= of pings Legality ; right action accompanied by ἘΠ _. 
a doing what is good because it is good, is Morality. ἐν a Pat 
this distinction, following the Stoical doctrine of mern — ἐπα 
1 etween incli 
i ty presupposes a struggle 
Development into morality ER 
ion of morality (according to Sc 
and duty; but the perfection o noral 5 
re lies in the harmony of inclination and duty; for (as — 
saw) what is best in itself in what is ethically produced en με : 
be most desirable, just as what is truly beautiful according to > τῷ 
n 
of Esthetics is the most agreeable. The harmony between = ina ne 
and duty is attained in its fullest measure in the exercise of the vo 
ti i ’s individual character. 
rresponding to one’s indivi | 
= = en of the duties and of their corresponding Er e 
fended on the different kinds of purposes —_— = > 
i dingly on the different kinds o 
roblem of mankind, and according é = 
a inclinations; but every single duty and virtue nn wa ᾿ 
cessary relation to the whole ethical task. The subor = . 
en which tend to advance our own eg er pes μιῇ 
? ΓῚ ΓῚ x a 5 
i i i lled rational self-regard ; 
nised by the ethical view 1s ca sails 
Bed of inclinations to advance others’ interests — the 
»jehk in 
ethical law is called rational love of our neighbour. The following 





590 Appendix D. 





virtues, which have as many classes of corresponding duties, are to be 
arranged (with Aristotle) by themselves : — Courage, Temperance, 
Generosity, Honour, Gentleness, Truth, Sociableness, Friendship, and 
Justice in the narrower sense of the word, which (according to 
Aristotle) is partly distributive, partly corrective, and this last has 
partly to do with reward, partly with punishment. ‘Distributive 
Justice’ has to do with the functions of legislation and administration ; 
‘Corrective Justice’ has reference to reward determined by an already 
existing order of rights, on which, in disputed cases, the judge must 
found his decision. Justice in the most comprehensive sense, which 
(according to Aristotle) is the chief virtue with reference to our fellow- 
men, may be identified with loyalty to duty. (The virtues called 
‘diametic’ by Aristotle are not virtues in the special sense of the 
word—i.e. with reference to the adaptability of the will). 

§ 9. Education is the formation of one capable of being trained to 
virtue; Instruction is training to intellectual and technical adapt- 
ability. The formation of principles lies in the (Aristotelian) axiom 
that the individual is to be led from the sensible, which is the earlier 
for us, to the intellectual, which is the first in itself, so that what is 
first in itself may come to have the predominance over what is first 
for us. 


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